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1)

 In a PQR, P is the largest angle and  cosp=13 . Further in circle of the triangle touches the sides PQ, QR and RP at 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) 24

D) 22

Answer:

Option B,D

Explanation:

Concept involved

 When ever cosine of angle and sides are given or to find out , we should always use cosine law

 i.e,    cosA=b2+c2a22bc

     cosB=a2+c2b22ac

cosC=a2+b2c22ba

1352021121_m4.JPG

   cosP=b2+c2a22bc

 13=(2n+4)2+(2n+2)2(2n+6)22(2n+4)(2n+2)

    (    cos P= 13)

 4n2168(n+1)(n+2)=13

  n242(n+1)(n+2)=13

   (n2)2(n+1)=13

     3n-6=2n+2  n=8

   sides are 2n+2, 2n+4,2n+6

  18,20,22