OSN 2022 Problem 6

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 $BPC$ .