Question

Find the measure of FG.

E
A
σ
9
6
A
Fx-3
H
G
x-2

Answer 1

B

Explanation:

GE and GA are secants from an external point G to the circle.

The product of the measures of one secant's external part and that entire secant is equal to the the product of the measures of the other secant's external part and that entire secant, that is

GF × GE = GH × GA ← substitute values

(x - 3)(x - 3 + 9) = (x - 2)(x - 2 + 6) , that is

(x - 3)(x + 6) = (x - 2)(x + 4) ← expand factors using FOIL

x² + 3x - 18 = x² + 2x - 8 ( subtract x² from both sides )

3x - 18 = 2x - 8 ( subtract 2x from both sides )

x - 18 = - 8 ( add 18 to both sides )

x = 10

Then

FG = x - 3 = 10 - 3 = 7