Let PQRS be a parallelogram and T be a point on diagonal QS such that ∠TRQ = ∠ PRS.
The circumcircle of triangle PQS intersects line PR at points P and U.
Find : ∠ PUS/∠ TUQ.

** Source: Serbia National Math Olympiad.

If PQRS is a rhombus, PR is a line of symmetry.
T is on PR and so the center of the rhombus.
U is on PR and so by symmetry ∠ PUS=∠ TUQ.

If we accept that this problem has a single solution were done.

But to truly finish we now need to show these angles are still equal without this extra symmetry.

Posted by Jer on 2015-09-26 22:07:17