Question

In ABC, N is the incenter, NE=8x-9, and ND=3x+6. Which of the measures are possible lengths of NG ?

Answer 1

To find the possible lengths of NG, we need to use the property that the incenter is equidistant from the sides of the triangle. The possible length of NG is 15.

Step-by-step explanation:

To find the possible lengths of NG, we need to use the property that the incenter is equidistant from the sides of the triangle. In triangle ABC, N is the incenter, NE is a distance from N to the side AE, and ND is a distance from N to the side AD.

Since NE = 8x - 9 and ND = 3x + 6, we can set up an equation:

NE = ND

8x - 9 = 3x + 6

Solving for x:

5x = 15

x = 3

Now we can find the possible lengths of NG. Substituting x = 3 into the expressions for NE and ND:

NE = 8(3) - 9 = 15

ND = 3(3) + 6 = 15

Therefore, the possible length of NG is 15.