Triangles BCD, ACG, and GDN are similar; all of them are 30-60-90
Let's denote the intersection point of AF and BD with a leter N
BN = 13 * tan(30°) = 7.505
DN = 1 / cos (30°) = 1.155
BD = BN + DN = 8.66
CD = BD / cos (30°) = 10
Circle radius r = CD / 2 = 5
EG = sqrt [ r² - ( r - 1 )² ] = 3
CG = CD - GD = 9
AG = CG / tan (30°) = 15.588
EA = AG - EG = 12.588