Given:
Point P is the incenter of triangle HKM.
To find:
The measure of JP.
Solution:
In triangle MNP, using Pythagoras theorem, we get
[tex]Hypotenuse^2=base^2+Perpendicular^2[/tex]
[tex](MP)^2=(MN)^2+(NP)^2[/tex]
[tex](25)^2=(24)^2+(NP)^2[/tex]
[tex]625=576+(NP)^2[/tex]
[tex]625-576=(NP)^2[/tex]
[tex]49=(NP)^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{49}=NP[/tex]
[tex]\pm 7=NP[/tex]
Side cannot be negative. So,
[tex]NP=7[/tex]
Point P is the incenter of triangle HKM.
[tex]JP=NP[/tex] [Incenter is equidistant from each side of triangle]
[tex]JP=7[/tex]
Therefore, the value of JP is 7 units.
