Problem 667: Intersecting Circles, Secant, Tangent, Metric Relations, Mind Map

The figure shows the intersecting circles O and O' at A and B and the secant CAD. CE and DE are tangent to circles O and O' at C and D, respectively. BE meets circle O' at F, DF extended meets CE at G. If CG = 5 and GE = 4, find DE.