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compass+straightedge construction of triangle given circumcircle

Source: Ukraine 1999 Grade 9 P4

May 10, 2021
geometryconstructioncircumcircle

Problem Statement

The bisectors of angles A,B,CA,B,C of a triangle ABCABC intersect the circumcircle of the triangle at A1,B1,C1A_1,B_1,C_1, respectively. Let PP be the intersection of the lines B1C1B_1C_1 and ABAB, and QQ be the intersection of the lines B1A1B_1A_1 and BCBC. Show how to construct the triangle ABCABC by a ruler and a compass, given its circumcircle, points PP and QQ, and the halfplane determined by PQPQ in which point BB lies.
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