Let AB be the diameter of larger circle and CD be the diameter of the smaller circle. Let P be the mid point of AC and Q be the midpoint of DB.

Let O be the mid point of PQ. Taking O as the center and OP as the radius draw a circle. Every point on this circle is equidistant from the larger and the smaller circle. Draw a radius from the larger circle. Point of intersection of the radius and in between circle will serve as the center.