Question

Find the measure of line f and g

Answer 1

In this case we use intersecting secant theorem  

According to this theorem, GF*GE = GH*GA

So,we plug in the values

(x-3)*(x-3+9) =(x-2)*(x-2+6)

(x-3)*(x+6) =(x-2)*(x+4)

x^2 +6x -3x -18 =x^2 +4x -2x -8

x^2 +3x -18 =x^2 +2x -8

x^2 +3x -18 -x^2 -2x +8 =0

x -10 =0

x=10

So,FG =x-3 = 10-3 =7