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Nonstandard incentre config

Source: Sharygin Correspondence Round 2024 P16

March 6, 2024
geometryincenter

Problem Statement

Let AA1,BB1,AA_1, BB_1, and CC1CC_1 be the bisectors of a triangle ABCABC. The segments BB1BB_1 and A1C1A_1C_1 meet at point DD. Let EE be the projection of DD to ACAC. Points PP and QQ on sides ABAB and BCBC respectively are such that EP=PD,EQ=QDEP = PD, EQ = QD. Prove that ∠PDB1=∠EDQ\angle PDB_1 = \angle EDQ.
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