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AD is Euler line of triangle IKL

Source: IGO 2021 Advanced P5

December 30, 2021
geometry

Problem Statement

Given a triangle ABCABC with incenter II. The incircle of triangle ABCABC is tangent to BCBC at DD. Let PP and QQ be points on the side BC such that ∠PAB=∠BCA\angle PAB = \angle BCA and ∠QAC=∠ABC\angle QAC = \angle ABC, respectively. Let KK and LL be the incenter of triangles ABPABP and ACQACQ, respectively. Prove that ADAD is the Euler line of triangle IKLIKL.
Proposed by Le Viet An, Vietnam
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