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Bosnia and Herzegovina 2022 IMO TST P1

Source:

May 22, 2022
geometrycircumcirclegeometric transformationreflection

Problem Statement

Let ABCABC be a triangle such that AB=ACAB=AC and ∠BAC\angle BAC is obtuse. Point OO is the circumcenter of triangle ABCABC, and MM is the reflection of AA in BCBC. Let DD be an arbitrary point on line BCBC, such that BB is in between DD and CC. Line DMDM cuts the circumcircle of ABCABC in E,FE,F. Circumcircles of triangles ADEADE and ADFADF cut BCBC in P,QP,Q respectively. Prove that DADA is tangent to the circumcircle of triangle OPQOPQ.
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