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midpoint of MN lies on the circumcircle of PQR, isosceles related

Source: The 1st SAFEST Olympiad 2019 p1

September 9, 2019
geometrymidpointcircumcircleisosceles

Problem Statement

Let ABCABC be an isosceles triangle with AB=ACAB = AC. Let ADAD be the diameter of the circumcircle of ABCABC and let PP be a point on the smaller arc BDBD. The line DPDP intersects the rays ABAB and ACAC at points MM and NN, respectively. The line ADAD intersects the lines BPBP and CPCP at points QQ and RR, respectively. Prove that the midpoint of MNMN lies on the circumcircle of PQRPQR
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