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Rays, incircle, angles...

Source: Rioplatense L-3 2022 #4

December 13, 2022
geometryincenter

Problem Statement

Let ABCABC be a triangle with incenter II. Let DD be the point of intersection between the incircle and the side BCBC, the points PP and QQ are in the rays IBIB and ICIC, respectively, such that ∠IAP=∠CAD\angle IAP=\angle CAD and ∠IAQ=∠BAD\angle IAQ=\angle BAD. Prove that AP=AQAP=AQ.
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