Question 8
Three circles of radius 1 have centers $A,C,E$, as shown. Line $HC$ is tangent to the circle centered at $A$, and $AF$ meets $HC$ at $P$. Find $PC$. As indicated by the circle incidences in the figure, each center lies on the other two circles, and $F$ is the lower intersection of the circles centered at $C$ and $E$.
