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angle chasing practice for Russian 8-graders

Source: Sharygin Geometry Olympiad 2015 Final 8.8

August 1, 2018
geometryangles

Problem Statement

Points C1,B1C_1, B_1 on sides AB,ACAB, AC respectively of triangle ABCABC are such that BB1⊥CC1BB_1 \perp CC_1. Point XX lying inside the triangle is such that ∠XBC=∠B1BA,∠XCB=∠C1CA\angle XBC = \angle B_1BA, \angle XCB = \angle C_1CA. Prove that ∠B1XC1=90o−∠A\angle B_1XC_1 =90^o- \angle A.
(A. Antropov, A. Yakubov)
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