Competition problem — Geometry — Maths Olympiad Prep

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.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.