Let P,Q,R be points on the same side of a line g in the plane. Let M and N be the feet of the perpendiculars from P and Q to g respectively. Point S lies between the lines PM and QN and satisfies and satisfies PM=PS and QN=QS. The perpendicular bisectors of SM and SN meet in a point R. If the line RS intersects the circumcircle of triangle PQR again at T, prove that S is the midpoint of RT. geometrycircumcirclemidpointperpendicular bisectorperpendicular