well first you need to find the angle at which the line AB makes with the horizontal (angle of ABX)

from the picture i attach, angle of ABX can be found by:

tan ABX = (AE - BD) / ED

tan ABX = (radius of larger circle - radius of smaller circle)/(radius of larger circle + radius of smaller circle)

tan ABX = (4-1)/4+1)

tan ABX = 3/5 = 0.6

ABX = 30.9637 degrees

from observation this will also be the angle of ACE:

sin ACE = AE / AC

sin 30.9637 = (radius of larger circle) / AC

AC = radius of larger circle/sin 30.9637

AC = 7.774603526 cm