Answer:
QM = 7 cm
Explanation:
Tangents to a circle from an external point are congruent.
The perimeter (P) is the sum of the sides of the triangle, that is
PL + LQ + QM + MR + RN + NP = 42
6 + LQ + QM + 8 + 8 + 6 = 42
LQ + QM + 28 = 42 ( subtract 28 from both sides )
LQ + QM = 14
Since LQ = QM , then
QM = 7