Three circles with centers a, b, and c are externally tangent to each other as shown in the figure. lines eg and dg are tangent to circle c at points f and d and intersect at point g. if each circle has a diameter of 6 inches, find the length of dg and the area enclosed by lines fg and gd, and arc fd. : ) plese

My solution to the problem is as follows:

EC = 15 ... draw CF = 6 (radius) ...use Pythagorean theorem to find EF. 

EF^2 + CF^2 = EC^2 
EF^2 = 15^2 - 6^2 = 189 EF = sq root 189 

triangle GDE is similar to CFE ... thus proportional 
GD / ED = CF / EF 
GD / 18 = 6 / (sq root 189) 
GD = 108 / (sq root 189)

I hope my answer has come to your help. God bless and have a nice day ahead!

The answer of the above is