Question

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

Answer 1

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.