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computational geometry, incenter lies on circumcircle

Source: 1990 ITAMO p2

January 31, 2020
geometryincentercircumcircle

Problem Statement

In a triangle ABCABC, the bisectors of the angles at BB and AA meet the opposite sides at PP and QQ, respectively. Suppose that the circumcircle of triangle PQCPQC passes through the incenter RR of △ABC\vartriangle ABC. Given that PQ=lPQ = l, find all sides of triangle PQRPQR.
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