Two Triangles of Equal Area on Either Side of an Angle Bisector

Let ABC be a triangle and let the angle bisector at vertex C intersect the circumcircle at R and the perpendicular bisectors of BC and AC at P and Q, respectively. Let the midpoints of BC and AC be S and T, respectively. Then RQT and RPS have equal area.

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See IMO 2007 shortlist geometry problem G1.
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