Problem

In a

\Delta PQR

P

is the largest angle and

\cos P = \frac{1}{3}

. Further in circle of the triangle touches the sides

PQ, QR

and

RP

RP

N, L

and

M

respectively, such that the lengths of

PN, QL

and

RM

are consecutive even integers. Then, possible length(s) of the side(s) of the triangle is (are) a. 16 b. 18 c. 20 d. 22