MathDB

5

Part of 2015 Turkey MO (2nd round)

Problems(1)

Cyclic quadrilateral

Source: Turkey National Olympiad 2015 P5

12/14/2015
In a cyclic quadrilateral ABCDABCD whose largest interior angle is DD, lines BCBC and ADAD intersect at point EE, while lines ABAB and CDCD intersect at point FF. A point PP is taken in the interior of quadrilateral ABCDABCD for which ∠EPD=∠FPD=∠BAD\angle EPD=\angle FPD=\angle BAD. OO is the circumcenter of quadrilateral ABCDABCD. Line FOFO intersects the lines ADAD, EPEP, BCBC at XX, QQ, YY, respectively. If ∠DQX=∠CQY\angle DQX = \angle CQY, show that ∠AEB=90∘\angle AEB=90^\circ.
geometrygeometry proposedcyclic quadrilateral