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Indian RMO 2011: Question 5

Source:

December 4, 2011
geometryincentertrigonometrygeometric transformationreflectionAMCAIME

Problem Statement

Let ABCABC be a triangle and let BB1,CC1BB_1,CC_1 be respectively the bisectors of ∠B,∠C\angle{B},\angle{C} with B1B_1 on ACAC and C1C_1 on ABAB, Let E,FE,F be the feet of perpendiculars drawn from AA onto BB1,CC1BB_1,CC_1 respectively. Suppose DD is the point at which the incircle of ABCABC touches ABAB. Prove that AD=EFAD=EF
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