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a point is good if 6 points are concyclic

Source: 2014 Sharygin Geometry Olympiad Final Round 10.4

August 3, 2018
geometryConcyclic

Problem Statement

Let ABCABC be a fixed triangle in the plane. Let DD be an arbitrary point in the plane. The circle with center DD, passing through AA, meets ABAB and ACAC again at points AbA_b and AcA_c respectively. Points Ba,Bc,CaB_a, B_c, C_a and CbC_b are defined similarly. A point DD is called good if the points Ab,Ac,Ba,Bc,CaA_b, A_c,B_a, B_c, C_a, and CbC_b are concyclic. For a given triangle ABCABC, how many good points can there be?
(A. Garkavyj, A. Sokolov )
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