Question 10
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 $\angle GMH = \angle OGK$.
Macedonian source version, translated in full:
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 $\angle GMH = \angle OGK$.
Supplemental illustration (AI-generated):
Macedonian source version, translated in full:
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 $\angle GMH = \angle OGK$.
Supplemental illustration (AI-generated):