Question 6
Three circles have centers $A,C,E$ and radius 1. Line $HQ$ is tangent to the circle centered at $A$; $AF$ meets $HC$ at $P$. Point $G$ lies beyond $Q$ on line $HQ$, and $PG=3$. Find $GM$. The figure specifies that $A,C,E$ lie on one another's circles, $F$ is the second intersection of the circles centered at $C,E$, and $M,A,C$ are collinear with $M$ on the circle centered at $A$.
