FKMO 2021 Problem 5

The incenter and $A$ -excenter of $\triangle{ABC}$ is $I$ and $O$ . The foot from $A,I$ to $BC$ is $D$ and $E$ . The intersection of $AD$ and $EO$ is $X$ . The circumcenter of $\triangle{BXC}$ is $P$ . Show that the circumcircle of $\triangle{BPC}$ is tangent to the $A$ -excircle if $X$ is on the incircle of $\triangle{ABC}$ .