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

Source: Canada Repêchage 2024/7a CMOQR

March 25, 2024
geometryorthocenterincenter

Problem Statement

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.
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