195,155 views
21 votes
21 votes
P is the incenter of triangle JKL, PN= 21, and ML=27. Find LO.

P is the incenter of triangle JKL, PN= 21, and ML=27. Find LO.-example-1
User Michael Rahenkamp
by
2.6k points

1 Answer

11 votes
11 votes

Given that, P is the incenter of the triangle.

Therefore, PN=MP=PO=21.

Consider the right angled triangle PLM.


\begin{gathered} PL^2=MP^2+ML^2 \\ PL^2=21^2+27^2 \\ PL=34.2 \end{gathered}

Consider the right angled triangle PLO.


\begin{gathered} LO^2=LP^2-PO^2 \\ LO^2=34.2^2-21^2 \\ LO=27 \end{gathered}

Thus, LO is 27.

User NelDav
by
2.6k points