OSN 2004 Problem 4

There exists 4 circles, $a,b,c,d$ , such that $a$ is tangent to both $b$ and $d$ , $b$ is tangent to both $a$ and $c$ , $c$ is both tangent to $b$ and $d$ , and $d$ is both tangent to $a$ and $c$ . Show that all these tangent points are located on a circle.