Question

I is the incenter of the triangle. AI=3x+7, BI=5x-11, CI=52-2x. What is value of x?

Answer 1

Explanation:

Given,

ABC is a triangle in which I is the incenter of the triangle.

Solution,

Since I is the incenter of the triangle.

Incenter is the point where three angle bisectors of the triangle meets.

so AI = BI = CI

`3x+7=5x-11\\5x-3x=7+11\\2x=18\\x=9`

So,

Thus the value of x is 9.

Answer 2

x = 9

Explanation:

The incenter of a triangle is the point of intersection of all the three interior angle bisectors.

The distance from the incenter to the sides of the triangle is equal.

Therefore: AI = BI = CI

Equate the measures of AI and BI, and solve for x:
⇒ AI = BI

⇒ 3x + 7 = 5x - 11

⇒ 3x + 7 -5x = 5x - 11 - 5x

⇒ -2x + 7 = -11

⇒ -2x + 7 - 7 = -11 - 7

⇒ -2x = -18

⇒ -2x ÷ -2 = -18 ÷ -2

⇒ x = 9