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Geometric inequality with excenters

Source: All-Russian MO Final stage 2023 9.4

April 23, 2023
geometry

Problem Statement

Given is a triangle ABCABC and a point XX inside its circumcircle. If IB,ICI_B, I_C denote the B,CB, C excenters, then prove that XB⋅XC<XIB⋅XICXB \cdot XC <XI_B \cdot XI_C.
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