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Equal angles again

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 12

May 31, 2009
geometrygeometric transformationreflectioncircumcircletrigonometrytrig identitiesLaw of Sines

Problem Statement

Let CL CL be a bisector of triangle ABC ABC. Points A1 A_1 and B1 B_1 are the reflections of A A and B B in CL CL, points A2 A_2 and B2 B_2 are the reflections of A A and B B in L L. Let O1 O_1 and O2 O_2 be the circumcenters of triangles AB1B2 AB_1B_2 and BA1A2 BA_1A_2 respectively. Prove that angles O1CA O_1CA and O2CB O_2CB are equal.
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