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Reflect incenter through side of isosceles triangle

Source: 2016 IMO Shortlist G4

July 19, 2017
geometryincenterreflectioncircumcirclegeometry solvedIMO ShortlistInversion

Problem Statement

Let ABCABC be a triangle with AB=AC≠BCAB = AC \neq BC and let II be its incentre. The line BIBI meets ACAC at DD, and the line through DD perpendicular to ACAC meets AIAI at EE. Prove that the reflection of II in ACAC lies on the circumcircle of triangle BDEBDE.
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