Question 86
Two tangents are drawn from a point $M$ to circle $k$, that touch it at points $G$ and $H$. If $O$ is the center of $k$ and $K$ is the orthocenter of the triangle $MGH$, prove that $\angle GMH = \angle OGK$.
Translation of the repeated Macedonian statement: Two tangents from $M$ touch circle $k$ at $G,H$. If $O$ is its center and $K$ is the orthocenter of triangle $MGH$, prove $\angle GMH=\angle OGK$.
Translation of the repeated Macedonian statement: Two tangents from $M$ touch circle $k$ at $G,H$. If $O$ is its center and $K$ is the orthocenter of triangle $MGH$, prove $\angle GMH=\angle OGK$.