PUMaC 2021 · 几何（B 组） · 第 8 题
PUMaC 2021 — Geometry (Division B) — Problem 8
题目详情
- Three circles, ω , ω , ω are drawn, with ω externally tangent to ω at C and internally tangent 1 2 3 3 1 to ω at D. Say also that ω ω intersect at points A, B. Suppose the radius of ω is 20 , the 2 1 2 1 radius of ω is 15 , and the radius of ω is 6 . Draw line CD, and suppose it meets AB at point 2 3 √ a b X. If AB = 24 , then CX can be written in the form , where a, b, c are positive integers c where b is square-free, and a, c are relatively prime. Find a + b + c. 1
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