IMO 2023 Shortlist G7

Let ABC be an acute, scalene triangle with orthocentre H. Let a be the line through the reflection of B with respect to ...

IMO 2023 Shortlist G7

Category: Geometry

Problem

Let ABC be an acute, scalene triangle with orthocentre H. Let a be the line through the reflection of B with respect to CH and the reflection of C with respect to BH. Lines b and c are defined similarly. Suppose lines a, b, and c determine a triangle T . Prove that the orthocentre of T , the circumcentre of T and H are collinear. (Ukraine)