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IMO Team Selection Contest I

Geometry Difficulty 7.8 National Olympiad, round 2 Prove it Estonia

Let $ABC$ be a triangle with $AB = AC \ne BC$ and let $I$ be its incenter. The line $BI$ meets $AC$ at $D$ , and the line through $D$ perpendicular to $AC$ meets $AI$ at $E$ . Prove that the reflection of $I$ in $AC$ lies on the circumcircle of triangle $BDE$ .

Solution

Solution. See IMO 2016 shortlist, problem G4.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.