Question

What is the radius of the inscribed circle of HJK?


There is a triangle HJK in which M, N and L are the points on the side HJ, side JK and side HK respectively. Segment HP is the angle bisectors of angle KHJ, segment JP is the angle bisectors of angle HJK, and segment KP is the angle bisectors of angle JKH. Segment HP, segment JP, and segment KP intersect each other at point P. Segment MP is perpendicular to side HJ, segment NP is perpendicular to side JK, and segment LP is perpendicular to side HK. The length of PM is 6x-14 and the length of LP is 3x+4.

A. 2

B. 6

C. 10

D. 22

Answer 1

The length of radius of the inscribed circle of HJK is: D. 22.

What is the Inscribed Circle of a Triangle?

An inscribed circle of a triangle is the circle contained inside a triangle, where all the three sides of the triangle are touches the circle. Thus, the distance of the center of this triangle is equal in measure, which is also the radius of the circle.

Therefore:

3x + 4 = 6x - 14 (equal radius)

Combine like terms

3x - 6x = -4 - 14

-3x = -18

x = -18/-3

x = 6

Length of radius of the inscribed circle of HJK = 3x + 4

Plug in the value of x

Radius = 3(6) + 4 = 22

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