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incenter lies on a chord of a circle passing through A and B

Source: IV Soros Olympiad 1997-98 R3 9.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 1, 2024
geometryincenter

Problem Statement

A circle is drawn through vertices AA and BB of triangle ABCABC, intersecting sides ACAC and BCBC at points MM and PP. It is known that the segment MPMP contains the center of the circle inscribed in ABCABC. Find MPMP if AB=cAB = c, BC=aBC = a, CA=bCA=b.
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