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Excenter incenter

Source: 2023 Thailand MO Day 1 P2

May 11, 2023
geometryincenterperpendicular bisector

Problem Statement

Let △ABC\triangle ABC which ∠ABC\angle ABC are right angle, Let DD be point on ABAB ( D≠A,BD \neq A , B ), Let EE be point on line ABAB which BB is the midpoint of DEDE, Let II be incenter of △ACE\triangle ACE and JJ be AA-excenter of △ACD\triangle ACD. Prove that perpendicular bisector of BCBC bisects IJIJ
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