TH-TMO 2019 Problem 1

Let $ABCDE$ be a convex pentagon with $\angle AEB=\angle BDC=90^o$ and line $AC$ bisects $\angle BAE$ and $\angle DCB$ internally. The circumcircle of $ABE$ intersects line $AC$ again at $P$ . (a) Show that $P$ is the circumcenter of $BDE$ . (b) Show that $A, C, D, E$ are concyclic.