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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
2 months, 4 weeks ago

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