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CentroAmerican 2015 #3

Source: 2015 CentroAmerican Math Olympiad #3

June 27, 2015
OMCCgeometrycyclic quadrilateralcircumcircle

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with AB<CDAB<CD, and let PP be the point of intersection of the lines ADAD and BCBC.The circumcircle of the triangle PCDPCD intersects the line ABAB at the points QQ and RR. Let SS and TT be the points where the tangents from PP to the circumcircle of ABCDABCD touch that circle.
(a) Prove that PQ=PRPQ=PR.
(b) Prove that QRSTQRST is a cyclic quadrilateral.
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