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St. Petersburg MO 2017 Grade 9 P2

Source: St. Petersburg MO 2017 Grade 9 P2

May 3, 2018
geometry

Problem Statement

Given a triangle ABCABC, there’s a point XX on the side ABAB such that 2BX=BA+BC2BX = BA + BC. Let YY be the point symmetric to the incenter II of triangle ABCABC, with respect to point XX. Prove that YIB⊥ABYI_B\perp AB where IBI_B is the BB-excenter of triangle ABCABC.
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