MathDB
RMM 2013 Problem 3

Source:

March 2, 2013
geometrycircumcirclegeometric transformationhomothetyreflection

Problem Statement

Let ABCDABCD be a quadrilateral inscribed in a circle ω\omega. The lines ABAB and CDCD meet at PP, the lines ADAD and BCBC meet at QQ, and the diagonals ACAC and BDBD meet at RR. Let MM be the midpoint of the segment PQPQ, and let KK be the common point of the segment MRMR and the circle ω\omega. Prove that the circumcircle of the triangle KPQKPQ and ω\omega are tangent to one another.
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