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NPC center lies on C-angle bisector - VI Soros Olympiad 1999-00 Round 1 10.3

Source:

May 21, 2024
geometryNine Point Circle

Problem Statement

he center of the circle passing through the midpoints of all sides of triangle ABCABC lies on the bisector of its angle CC. Find the side ABAB if BC=aBC = a, AC=bAC = b (aa is not equal to bb).