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Annual Harvard-MIT Mathematics Tournament

Geometry Difficulty 4.5 AIME Prove it United States

Problem:

Let $ABC$ be a triangle, and $I$ its incenter. Let the incircle of $ABC$ touch side $BC$ at $D$ , and let lines $BI$ and $CI$ meet the circle with diameter $AI$ at points $P$ and $Q$ , respectively. Given $BI = 6$ , $CI = 5$ , $DI = 3$ , determine the value of $(DP / DQ)^2$ .

Solution

Solution:

Answer: $\frac{75}{64}$ Same as Geometry Test problem 9.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.