Rumusnya:
sudut yang dibentuk oleh perpotongan garis singgung 2, 2 secants atau 1
tangen dan 1 garis potong di luar lingkaran sama dengan setengah
perbedaan busur dicegat ! Oleh karena itu untuk menemukan sudut ini (angle K dalam contoh di bawah), semua yang harus Anda lakukan adalah mengambil jauh busur dicegat dan dekat busur dicegat kecil dan kemudian membagi jumlahnya dengan dua! Itu sebabnya kami menyebutnya Teorema Arc Jauh Dekat Arc
cara mudah untuk mengingat rumus
![](http://www.mathwarehouse.com/geometry/circle/images/thumbs/picture-power-of-point-2-secants-angle.png)
![](http://www.mathwarehouse.com/geometry/circle/images/thumbs/picture-power-of-point-tan-secant-angle3.png)
![](http://www.mathwarehouse.com/geometry/circle/images/thumbs/picture-power-of-point-2-tangents-angle.png)
Ukuran dari sudut yang dibentuk oleh garis potong dan garis singgung ditarik dari titik LUAR lingkaran adalah setengah selisih busur disadap .
Ingat bahwa teorema ini hanya menggunakan busur dicegat. Oleh karena itu, busur merah pada gambar di bawah tidak digunakan dalam formula ini.
![Gambar, Tangent & sekan picture of intersection of secant and a tangent](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/tangent-secant-picture.gif)
![Kekuatan Titik](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/what-is-measure-angle-x.jpg)
![](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/tangent-secant-picture-explanation.jpg)
Soal 2) Apakah ukuran overparen rmCH?
Hanya satu dari dua lingkaran BAWAH termasuk persimpangan dari garis singgung dan garis potong a.
Dapatkah Anda mencari tahu yang mana?
Teorema: Ukuran sudut yang dibentuk oleh dua garis singgung ditarik dari titik LUAR lingkaran adalah setengah selisih busur dicegat
Teorema ini berbeda dari dua lainnya pada halaman ini dalam setiap bagian dari lingkaran termasuk dalam busur disadap. Karena kedua garis adalah garis singgung, mereka menyentuh lingkaran di satu titik dan karena itu mereka tidak 'memotong' bagian-bagian lingkaran.
Masalah 3) Apa ukuran x pada gambar di sebelah kiri. (Kedua garis dalam gambar yang bersinggungan dengan lingkaran)
Soal 4) Apa ukuran overparent rmCH?
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0070.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0048.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0064.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0074.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0064.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0074.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0070.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0048.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0033.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0070.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0070.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png)
Soal 5) Dua secants memperpanjang dari titik yang sama dan memotong lingkaran seperti ditunjukkan dalam diagram di bawah. Apa nilai x?
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0048.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0064.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0074.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0064.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0074.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0070.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0048.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0033.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0070.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
Jauh Arc - dekat Arc Formula
Semua formula pada halaman ini dapat dianggap dalam hal "jauh busur" dan "dekat busur". Sudut yang dibentuk di luar lingkaran selalu sama dengan busur jauh dikurangi busur dekat dibagi 2.
![Jauh Arc dekat rumus busur](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/far-arc-near-arc-formula-picture-small.png)
cara mudah untuk mengingat rumus
![](http://www.mathwarehouse.com/geometry/circle/images/thumbs/picture-power-of-point-2-secants-angle.png)
![](http://www.mathwarehouse.com/geometry/circle/images/thumbs/picture-power-of-point-tan-secant-angle3.png)
![](http://www.mathwarehouse.com/geometry/circle/images/thumbs/picture-power-of-point-2-tangents-angle.png)
Tangent dan sekan dari titik Teorema
![](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/farc-narc-formula-tangent-secant.png)
![Tangent Dan sekan Diagram Picture of intersection of tangent and secant](http://www.mathwarehouse.com/geometry/circle/images/thumbs/picture-power-of-point-tan-secant-angle.gif)
Ingat bahwa teorema ini hanya menggunakan busur dicegat. Oleh karena itu, busur merah pada gambar di bawah tidak digunakan dalam formula ini.
Masalah Praktek
Soal 1)Gunakan teorema untuk persimpangan garis singgung dan garis potong untuk menemukan ukuran sudut yang dibentuk oleh perpotongan garis singgung dan garis potong tersebut.
![Gambar, Tangent & sekan picture of intersection of secant and a tangent](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/tangent-secant-picture.gif)
![Kekuatan Titik](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/what-is-measure-angle-x.jpg)
![](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/tangent-secant-picture-explanation.jpg)
Soal 2) Apakah ukuran
![](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/tangent-secant-diagram.gif)
Hanya satu dari dua lingkaran BAWAH termasuk persimpangan dari garis singgung dan garis potong a.
Dapatkah Anda mencari tahu yang mana?
![](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/rule-brain-teaser-Ans.jpg)
Dua Tangents dari Point
![](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/farc-narc-formula-tangent-tangent.gif)
![Dua Tangents Picture of intersection of two tangents](http://www.mathwarehouse.com/geometry/circle/images/thumbs/picture-power-of-point-2-tangents-angle.gif)
Teorema ini berbeda dari dua lainnya pada halaman ini dalam setiap bagian dari lingkaran termasuk dalam busur disadap. Karena kedua garis adalah garis singgung, mereka menyentuh lingkaran di satu titik dan karena itu mereka tidak 'memotong' bagian-bagian lingkaran.
Masalah 3) Apa ukuran x pada gambar di sebelah kiri. (Kedua garis dalam gambar yang bersinggungan dengan lingkaran)
![gambar dua garis singgung lingkaran](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/two-tangents/picture.jpg)
Soal 4) Apa ukuran
![](http://www.mathwarehouse.com/geometry/circle/images/power-of-point/two-tangents/image.png)
Dua berpotongan secants dari Point a
Ukuran sudut yang dibentuk oleh dua secants diambil dari titik di luar lingkaran adalah setengah perbedaan busur disadap. (Jauh busur - busur dekat)Pada gambar di bawah, ukuran sudut x adalah setengah perbedaan busur dicegat oleh dua secants
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0070.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0048.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0043.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0048.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0033.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0076.png)
![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Math/Italic/120/0070.png)
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![](http://cdn.mathjax.org/mathjax/2.1-latest/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png)
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Soal 5) Dua secants memperpanjang dari titik yang sama dan memotong lingkaran seperti ditunjukkan dalam diagram di bawah. Apa nilai x?
![Diagram persimpangan dua secants lingkaran](http://www.mathwarehouse.com/geometry/circle/images/two-secants/diagram-intersection-of-secants.png)
Brain Teaser
![]() | Menggunakan pengetahuan Anda tentang teorema di halaman ini untuk menentukan apakah titik C atau titik D adalah di mana segmen bawah memotong lingkaran . Dengan kata lain, adalah D titik singgung ke lingkaran? |
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