Question

In the figure shown, GD = 3x + 5, GF = 6x-4, and G is the incenter of AABC. Find GE

Answer 1

GE = 14

Explanation:

The incenter is equidistant from the sides, so GD = GE = GF.

Set the expressions for GD and GF equal to each other and solve for x.

3x + 5 = 6x - 4

5 = 3x - 4

9 = 3x

3 = x

Now plug this value into either expression, say for GD. GD = 3(3) + 5 = 14.

GE must be the same, GE = 14