Mathematics: Point P is the incenter of HKM. Find JP

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Point P is the incenter of HKM. Find JP - id10286366, davisnaziyahovz5sk

rjsimpson73

16.03.2022

Given:

Point P is the incenter of triangle HKM.

To find:

The measure of JP.

Solution:

In triangle MNP, using Pythagoras theorem, we get

Hypotenuse^2=base^2+Perpendicular^2

(MP)^2=(MN)^2+(NP)^2

(25)^2=(24)^2+(NP)^2

625=576+(NP)^2

625-576=(NP)^2

49=(NP)^2

Taking square root on both sides, we get

$\pm \sqrt{49}=NP$

$\pm 7=NP$

Side cannot be negative. So,

NP=7

Point P is the incenter of triangle HKM.

JP=NP [Incenter is equidistant from each side of triangle]

JP=7

Therefore, the value of JP is 7 units.

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