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Similar to P:11.2

Source: All Russian 2014 Grade 9 Day 2 P2

May 3, 2014
geometrytrapezoidsymmetrygeometry proposed

Problem Statement

Let ABCDABCD be a trapezoid with AB∥CDAB\parallel CD and Ω \Omega is a circle passing through A,B,C,DA,B,C,D. Let ω \omega be the circle passing through C,DC,D and intersecting with CA,CBCA,CB at A1A_1, B1B_1 respectively. A2A_2 and B2B_2 are the points symmetric to A1A_1 and B1B_1 respectively, with respect to the midpoints of CACA and CBCB. Prove that the points A,B,A2,B2A,B,A_2,B_2 are concyclic.
I. Bogdanov
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