UPSC NDA I 2023 Mathematics Solved Paper

Consider the following for the next two (02) items that follow :
In a triangle PQR,P is the largest angle and cos‌P=‌

1

3

. Further the in-circle of the triangle touches the sides PQ,QR and RP at N,L and M respectively such that the lengths PN,QL and RM are n,n+2,n+4 respectively where n is an integer.