MathDB

12

Part of 2009 Sharygin Geometry Olympiad

Problems(1)

Equal angles again

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

5/31/2009
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.
geometrygeometric transformationreflectioncircumcircletrigonometrytrig identitiesLaw of Sines