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triangles defined on circle, area sums

Source: Ukraine 1998 Grade 10 P6

June 5, 2021
geometryareasTrianglecircles

Problem Statement

Let ABAB and CDCD be diameters of a circle with center OO. For a point MM on a shorter arc CBCB, lines MAMA and MDMD meet the chord BCBC at points PP and QQ respectively. Prove that the sum of the areas of the triangles CPMCPM and MQBMQB equals the area of triangle DPQDPQ.
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