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Equal Angles

Source: Sharygin geometry olympiad 2016, grade 10, Final Round, Problem 2

August 5, 2016
geometryincentercircumcircle

Problem Statement

Let II and IaI_a be the incenter and excenter (opposite vertex AA) of a triangle ABCABC, respectively. Let A′A' be the point on its circumcircle opposite to AA, and A1A_1 be the foot of the altitude from AA. Prove that ∠IA1Ia=∠IA′Ia\angle IA_1I_a=\angle IA'I_a.
(Proposed by Pavel Kozhevnikov)
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