We are given a triangle $JKL$ that is circumscribed around a circle $Q$. We are given the lengths $KM = 8$ m, $LP = 11$ m, and $JM = 18$ m. We need to find the perimeter of triangle $JKL$.

1. Problem Description

We are given a triangle $JKL$ that is circumscribed around a circle $Q$. We are given the lengths $KM = 8$ m, $LP = 11$ m, and $JM = 18$ m. We need to find the perimeter of triangle $JKL$.

2. Solution Steps

The key property to use here is that tangents from a point to a circle have equal lengths. This means that:

$KM = KN$

$LP = LN$

$JP = JM$

Since $KM = 8$ m, we have $KN = 8$ m.

Since $LP = 11$ m, we have $LN = 11$ m.

Since $JM = 18$ m, we have $JP = 18$ m.

Now, we can find the lengths of the sides of the triangle:

$JK = JM + MK = 18 + 8 = 26$ m

$JL = JP + PL = 18 + 11 = 29$ m

$KL = KN + NL = 8 + 11 = 19$ m

Finally, we find the perimeter of triangle $JKL$ by adding the lengths of its sides:

Perimeter = $JK + JL + KL = 26 + 29 + 19 = 74$ m

3. Final Answer

Perimeter of $JKL = 74$ m