Mathematics - Properties of Triangle Question with Solution | TestHub

The distance between the circumcenter ($O$) and the orthocenter ($H$) in a triangle is given by Euler's theorem.

The formula for $O{H}^2$ is $O{H}^2=R^2(1-8\cos A\cos B\cos C)$. This formula is valid for any triangle, but the problem specifies an acute-angled triangle, which ensures$\cos A,\cos B,\cos C$ are all positive.