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PB is perpendicular to MK - Iran NMO 2005 - Problem5

Source:

September 21, 2010
geometryparallelogramtrapezoidgeometry proposed

Problem Statement

BCBC is a diameter of a circle and the points X,YX,Y are on the circle such that XY⊥BCXY\perp BC. The points P,MP,M are on XY,CYXY,CY (or their stretches), respectively, such that CY∣∣PBCY||PB and CX∣∣PMCX||PM. Let KK be the meet point of the lines XC,BPXC,BP. Prove that PB⊥MKPB\perp MK.
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