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2 circumcircles intersect on angle bisector, equal segments in extensions

Source: 2013 Oral Moscow Geometry Olympiad grades 8-9 p4

August 14, 2019
geometrycircumcircleangle bisectorequal segmentsconcurrencyconcurrent

Problem Statement

Let ABCABC be a triangle. On the extensions of sides ABAB and CBCB towards BB, points C1C_1 and A1A_1 are taken, respectively, so that AC=A1C=AC1AC = A_1C = AC_1. Prove that circumscribed circles of triangles ABA1ABA_1 and CBC1CBC_1 intersect on the bisector of angle BB.
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