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Prove that the circumcentre of AB_1C_1 lies on the line AO_1

Source: Tuymaada 2009, Senior League, Second Day, Problem 3

July 19, 2009
geometry

Problem Statement

A triangle ABC ABC is given. Let B1 B_1 be the reflection of B B across the line AC AC, C1 C_1 the reflection of C C across the line AB AB, and O1 O_1 the reflection of the circumcentre of ABC ABC across the line BC BC. Prove that the circumcentre of AB1C1 AB_1C_1 lies on the line AO1 AO_1. Proposed by A. Akopyan
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