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Found problems: 1

2024 Iranian Geometry Olympiad, 4
Tags: IGO , 2024 , IGO 2024 , Cool problem , geometry
Point $P$ is inside the acute triangle $\bigtriangleup ABC$ such that $\angle BPC=90^{\circ}$ and $\angle BAP=\angle PAC$. Let $D$ be the projection of $P$ onto the side $BC$. Let $M$ and $N$ be the incenters of the triangles $\bigtriangleup ABD$ and $\bigtriangleup ADC$ respectively. Prove that the quadrilateral $BMNC$ is cyclic. [i]Proposed by Hussein Khayou - Syria[/i]