ABD triangle
ED = 8
CD = ?
C is center of internal circumference
with radius R = EC
ED = 8 = EC + CD
EC = 8 - CD
EC = CG
CD^2 = EC^2 + GD^2
GD = CD • cos 30°
cos 30 = √3/2
Then
CD^2 - (8 - CD )^2 = CD^2 • cos 30^2
Then
(2CD - 8) •8 = CD^2•(3/4)
16CD - 64 = CD^2•(3/4)
Then ANSWER IS
CD = 5.33