OMA 2014 Problem 3

Two circumferences of radius $1$ that do not intersect, $c_1$ and $c_2$ , are placed inside an angle whose vertex is $O$ . $c_1$ is tangent to one of the rays of the angle, while $c_2$ is tangent to the other ray. One of the common internal tangents of $c_1$ and $c_2$ passes through $O$ , and the other one intersects the rays of the angle at points $A$ and $B$ , with $AO=BO$ . Find the distance of point $A$ to the line $OB$ .