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isosceles wanted, incenters and perpendicular bisector related

Source: 2014 Saudi Arabia Pre-TST 3.3

September 12, 2020
geometryincenterperpendicular bisectorisosceles

Problem Statement

Let ABCABC be a triangle and II its incenter. The line AIAI intersects the side BCBC at DD and the perpendicular bisector of BCBC at EE. Let JJ be the incenter of triangle CDECDE. Prove that triangle CIJCIJ is isosceles.
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