Mathematics - Properties of Triangle Question with Solution | TestHub

Let $AD$ be the altitude from $A$ to $BC$. In $△ABD$, $AD=c\sin B$. The orthocenter $H$ lies on $AD$. Consider the circumcircle of $△ABC$. Let $O$ be the circumcenter. The distance from $O$ to $BC$ is $R\cos A$. The distance from $A$ to $H$ (orthocenter) is $AH=2R\cos A$. This is a standard property relating the orthocenter, circumradius, and angles of a triangle.