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Isosceles triangle

Source: SMO(O) 2007 #3

January 18, 2015
geometrycircumcirclegeometry unsolved

Problem Statement

Let A1A_1, B1B_1 be two points on the base ABAB of an isosceles triangle ABCABC, with ∠C>60∘\angle C>60^{\circ}, such that ∠A1CB1=∠ABC\angle A_1CB_1=\angle ABC. A circle externally tangent to the circumcircle of △A1B1C\triangle A_1B_1C is tangent to the rays CACA and CBCB at points A2A_2 and B2B_2, respectively. Prove that A2B2=2ABA_2B_2=2AB.
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