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Prove that two circumcircle intersect on a line

Source: 2022 Thailand Online MO P8

April 4, 2022
geometrycircumcircle

Problem Statement

Let ABCDABCD be a convex quadrilateral with AD=BCAD = BC, ∠BAC+∠DCA=180∘\angle BAC+\angle DCA = 180^{\circ}, and ∠BAC≠90∘.\angle BAC \neq 90^{\circ}. Let O1O_1 and O2O_2 be the circumcenters of triangles ABCABC and CADCAD, respectively. Prove that one intersection point of the circumcircles of triangles O1BCO_1BC and O2ADO_2AD lies on ACAC.
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