Question

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. :) help pleaaaaaaaase

Answer 1

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!