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length of segment of intersections of pairs of external angle bisectors = s

Source: Mexican Mathematical Olympiad 1999 OMM P5

July 28, 2018
geometryAngle Bisectors

Problem Statement

In a quadrilateral ABCDABCD with AB//CDAB // CD, the external bisectors of the angles at BB and CC meet at PP, while the external bisectors of the angles at AA and DD meet at QQ. Prove that the length of PQPQ equals the semiperimeter of ABCDABCD.
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