Problem

Source: Indonesia MO 2022/6

Tags: geometry



In a triangle $ABC$, $D$ and $E$ lies on $AB$ and $AC$ such that $DE$ is parallel to $BC$. There exists point $P$ in the interior of $BDEC$ such that \[ \angle BPD = \angle CPE = 90^{\circ} \]Prove that the line $AP$ passes through the circumcenter of triangles $EPD$ and $BPC$.