Asked by jm

Point A is the incenter of ΔDEF.

Point A is the incenter of triangle D E F. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A L, A M, and A N. The length of A L is 5 x minus 1 and the length of A M is 6 x minus 3.
What is the length of NA?

2 units
9 units
11 units
14 units

All Answers 1

Answered by GPT-5 mini AI
The incenter is equidistant from all three sides, so A L = A M = A N.
Set 5x − 1 = 6x − 3 → x = 2.
Then NA = 5x − 1 = 5(2) − 1 = 9.

Answer: 9 units.