MathDB
AT=RC [Baltic way 2003]

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November 7, 2010
geometry proposedgeometry

Problem Statement

The diagonals of a cyclic convex quadrilateral ABCDABCD intersect at PP. A circle through PP touches the side CDCD at its midpoint MM and intersects the segments BDBD and ACAC again at the points QQ and RR respectively. Let SS be the point on segment BDBD such that BS=DQBS = DQ. The line through SS parallel to ABAB intersects ACAC at TT. Prove that AT=RCAT = RC.
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