Question 35
Let $\overline{BD}$ and $\overline{CE}$ be the altitudes of an acute-angled triangle $ABC$. The circle with diameter $\overline{AC}$ meets $\overline{BD}$ at $F$. The circle with diameter $\overline{AB}$ meets the line $CE$ at points $G$ and $H$, where $G$ is between $C$ and $E$. If $\angle CHF = 12^\circ$, find the measure of the angle $\angle AGF$. (Go Geometry)