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Circle joining centers tangent to original circumcircle

Source: Sharygin 2015 Finals Grade 9 Problem 8

July 22, 2018
geometrycircumcircle

Problem Statement

A perpendicular bisector of side BCBC of triangle ABCABC meets lines ABAB and ACAC at points ABA_B and ACA_C respectively. Let OaO_a be the circumcenter of triangle AABACAA_BA_C. Points ObO_b and OcO_c are defined similarly. Prove that the circumcircle of triangle OaObOcO_aO_bO_c touches the circumcircle of the original triangle.
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