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Incenter and Square of Ratio

Source: HMMT 2008 Geometry Problem 9

March 9, 2008
geometryincenterratioangle bisector

Problem Statement

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