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find area of triangle formed by segments of circumcircle

Source: Mongolian MO 2007 Teachers P5

April 8, 2021
geometrycircumcircle

Problem Statement

Given a point PP in the circumcircle ω\omega of an equilateral triangle ABCABC, prove that the segments PAPA, PBPB, and PCPC form a triangle TT. Let RR be the radius of the circumcircle ω\omega and let dd be the distance between PP and the circumcenter. Find the area of TT.
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