Let ABCD be a rectangle with AB<BC and circumcircle Γ. Let P be a point on the arc BC (not containing A) and let Q be a point on the arc CD (not containing A) such that BP=CQ.The circle with diameter AQ intersects AP again in S. The perpendicular to AQ through B intersects AP in X.
(a) Show that XS=PS.
(b) Show that AX=DQ. geometry proposedgeometryrectanglecircumcircle