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# Ortho-circumcentric complexity

Consider an acute-angled triangle $$ABC$$, with circumcenter $$O$$.

Denote the point $$D$$ such that it lies on segment $$BC$$.
Let $$O_{1}$$ and $$O_{2}$$ be the circumcentres of triangle $$ABD$$ and $$ACD$$, respectively.

Consider the triangle $$O_{1}O_{2}D$$, with orthocenter $$H_1$$.

Prove that: $$O H_{1}$$ is parallel to $$BC$$.

Bonus: Prove this result for an obtuse-angled triangle as well.

Note by Neel Khare
7 months ago