Question

N is the in center of △ABC. Use the given information to find NS. NQ=2x NR=3x−2

Answer 1

Given that N is the incenter of △ABC, NS = 4.

What is the Incenter of a Triangle?

• The incenter of a triangle is the point of concurrency of the three angle bisectors of a triangle.
• The perpendicular distances from each sides of the triangle to the incenter are equal.

Given the image where:

NQ = 2x

NR = 3x − 2

NQ = NR = NS (equidistant from the incenter)

Thus:

2x = 3x - 2

• Add like terms

2x - 3x = -2

-x = -2

x = 2

NQ = NS = 2x

• Plug in the value of x

NS = 2(2)

NS = 4

Therefore, given that N is the incenter of △ABC, NS = 4.

Learn more about the incenter on:

brainly.com/question/1831482