MathDB
Config geo with a weird circle

Source: Baltic Way 2022/14

November 12, 2022
geometry

Problem Statement

Let Γ\Gamma denote the circumcircle and OO the circumcentre of the acute-angled triangle ABCABC, and let MM be the midpoint of the segment BCBC. Let TT be the second intersection point of Γ\Gamma and the line AMAM, and DD the second intersection point of Γ\Gamma and the altitude from AA. Let further XX be the intersection point of the lines DTDT and BCBC. Let PP be the circumcentre of the triangle XDMXDM. Prove that the circumcircle of the triangle OPDOPD passes through the midpoint of XDXD.
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