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Found problems: 1

Kyiv City MO Seniors Round2 2010+ geometry, 2019.10.3.1
Tags: equal segments , geometry , pentagon , regular pentagon
Let $ABCDE$ be a regular pentagon with center $M$. Point $P \ne M$ is selected on segment $MD$. The circumscribed circle of triangle $ABP$ intersects the line $AE$ for second time at point $Q$, and a line that is perpendicular to the $CD$ and passes through $P$, for second time at the point $R$. Prove that $AR = QR$.