MathDB
Nice geometry problem

Source: Problem 1 from ZIMO 2008

January 21, 2008
geometryrhombusgeometry proposed

Problem Statement

Points K,L,M,N K,L,M,N are repectively the midpoints of sides AB,BC,CD,DA AB,BC,CD,DA in a convex quadrliateral ABCD ABCD.Line KM KM meets dioganals AC AC and BD BD at points P P and Q Q,respectively.Line LN LN meets dioganals AC AC and BD BD at points R R and S S,respectively. Prove that if AP\cdot PC\equal{}BQ\cdot QD,then AR\cdot RC\equal{}BS\cdot SD.
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