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Angle Ratio Ascertainment 2 (Posted on 2015-09-26) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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A simpler problem | Comment 1 of 2
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
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