Draw the line joining the two center of the circles. Draw the two circles as you have mentioned. Let R be the radius of the bigger circle. Let R1, R2 and R3 be radii of the three circles in a line from left to right. Draw a perpendicular line to the line joining the centers through the center of the middle circle.
The centers of the remaining two circles must line on the perpendicular line.
Centers of middle circle, right side circle and new bottom circle form a right angled triangle. So
(R2^2 + R4^2) + (R2^2 + R3^2) = (R3^2+ R4^2)
Solving this you can find R4 = R5.