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circumcenter of AXY lies on circumcircle of ABC

Source: 2023 Thailand Online MO P6

February 12, 2023
geometry

Problem Statement

Let ABCABC be a triangle. Construct point XX such that BX=BABX=BA and XX and CC lies on the same side of line ABAB. Construct point YY such that CY=CACY=CA and YY and BB lies on different sides of line ACAC. Suppose that triangle BAXBAX and triangle CAYCAY are similar, prove that the circumcenter of triangle AXYAXY lies on the circumcircle of triangle ABCABC.
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