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.

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