Question

Please Help (98 POINTS)!

Answer 1

Angle-Bisector theorem:

(x+3)/(x+10) = (x -3)/(x +1)

Cross multiply

(x+3)(x +1) = (x+10)(x -3)

x^2 + 3x + x + 3 = x^2 + 10x -3x - 30

4x + 3 = 7x - 30

- 3x = -33

x = 11

DF = x - 3 + x + 1

DF = 2x - 2

DF = 2(11) - 2

DF = 22 - 2

DF = 20

Answer

DF = 20 units

Answer 2

Since GE bisects the angle, we can use the angle bisector theorem

DE/EF = GD/GF

x-3/(x+1) = (x+3)/(x+10)

using cross products

(x-3) (x+10) = (x+1) (x+3)

FOIL

x^2 -3x+10x-30 = x^2 +x+3x+3

combine like terms

x^2 +7x-30 = x^2 +4x+3

subtract x^2 from each side

7x-30 = 4x+3

subtract 4x from each side

3x-30 = 3

add 30 to each side

3x =33

divide by 3

x=11

DF = (x-3+ (x+1)+

DF = 2x-2

= 2(11) -2

= 22-2

= 20