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$Q$ and $R$ are respectively the incenters in the triangles

Source: GMB-IMAR 2005, Juniors, Problem 2

October 10, 2005
geometryincentergeometry proposed

Problem Statement

Let PP be an arbitrary point on the side BCBC of triangle ABCABC and let DD be the tangency point between the incircle of the triangle ABCABC and the side BCBC. If QQ and RR are respectively the incenters in the triangles ABPABP and ACPACP, prove that ∠QDR\angle QDR is a right angle. Prove that the triangle QDRQDR is isosceles if and only if PP is the foot of the altitude from AA in the triangle ABCABC.
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