equation of circle
2011-06-02 1:46 am
圖片參考：http://img94.imageshack.us/img94/7246/98349639.jpg
In the figure, the inscribed circle of ΔOPQ touches PQ at R. Find the coordinates of R.
回答 (1)
2011-06-02 2:50 am
✔ 最佳答案
Let radius of circle be r. By property of tangents to circle, QR = 5 - r.
PR = 12 - r.
So PQ = (5 - r) + (12 - r) = 17 - 2r.
By Pythagoras thm., PQ = sqrt (5^2 + 12^2) = 13
That is 17 - 2r = 13
r = 2.
So QR = 5 - 2 = 3
PR = 12 - 2 = 10.
So QR : RP = 3 : 10
So x - coordinate of R = [(12)(3) + (10)(0)]/(10 + 3) = 36/13.
y - coordinate of R = [(0)(3) + (5)(10)]/(10 + 3) = 50/13.
So R is (36/13, 50/13).
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110601000051KK00609