PL-OM 2009 Problem 5

A sphere is inscribed in tetrahedron $ABCD$ and is tangent to faces $BCD,CAD,ABD,ABC$ at points $P,Q,R,S$ respectively. Segment $PT$ is the sphere's diameter, and lines $TA,TQ,TR,TS$ meet the plane $BCD$ at points $A',Q',R',S'$ . respectively. Show that $A$ is the center of a circumcircle on the triangle $S'Q'R'$ .