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If the resulting quad is cyclic, then ABC must be isosceles

Source: Czech-Polish-Slovak 2003 Q4

April 28, 2013
geometry unsolvedgeometry

Problem Statement

Point PP lies on the median from vertex CC of a triangle ABCABC. Line APAP meets BCBC at XX, and line BPBP meets ACAC at YY . Prove that if quadrilateral ABXYABXY is cyclic, then triangle ABCABC is isosceles.
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