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equal angles starting with angles bisectors

Source: 2007 Sharygin Geometry Olympiad Correspondence Round P15

April 27, 2019
geometryequal anglesAngle Bisectors

Problem Statement

In a triangle ABCABC, let AA′,BB′AA', BB' and CC′CC' be the bisectors. Suppose A′B′∩CC′=PA'B' \cap CC' =P and A′C′∩BB′=QA'C' \cap BB'= Q. Prove that ∠PAC=∠QAB\angle PAC = \angle QAB.
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