RIOPLATENSE 1997 Problem 4

Circles $c_1$ and $c_2$ are tangent internally to circle $c$ at points $A$ and $B$ , respectively, as seen in the figure. The inner tangent common to $c_1$ and $c_2$ touches these circles in $P$ and $Q$ , respectively. Show that the $AP$ and $BQ$ lines intersect the circle $c$ at diametrically opposite points.