ILL 1982 Problem 25

Four distinct circles $C,C_1, C_2$ , C3 and a line L are given in the plane such that $C$ and $L$ are disjoint and each of the circles $C_1, C_2, C_3$ touches the other two, as well as $C$ and $L$ . Assuming the radius of $C$ to be $1$ , determine the distance between its center and $L.$