MathDB

7a

Part of 2024 Canadian Mathematical Olympiad Qualification

Problems(1)

AH //BC iff orthocenter H of BIC lies on circle (AI), where I incenter

Source: Canada Repêchage 2024/7a CMOQR

3/25/2024
In triangle ABCABC, let II be the incentre. Let HH be the orthocentre of triangle BICBIC. Show that AHAH is parallel to BCBC if and only if HH lies on the circle with diameter AIAI.
geometryorthocenterincenter