IGO 2021 E3

As shown in the following figure, a heart is a shape consist of three semicircles with diameters $AB$ , $BC$ and $AC$ such that $B$ is midpoint of the segment $AC$ . A heart $\omega$ is given. Call a pair $(P, P')$ bisector if $P$ and $P'$ lie on $\omega$ and bisect its perimeter. Let $(P, P')$ and $(Q,Q')$ be bisector pairs. Tangents at points $P, P', Q$ , and $Q'$ to $\omega$ construct a convex quadrilateral $XYZT$ . If the quadrilateral $XYZT$ is inscribed in a circle, find the angle between lines $PP'$ and $QQ'$ .

Proposed by Mahdi Etesamifard - Iran