In a triangle $P Q R, P$ is the largest angle and $\cos P=\frac{1}{3}$. Further the incircle of the triangle touches the sides $P Q, Q R$ and $R P$ at $N, L$ and $M$ respectively, such that the lengths of $P N, Q L$ and $R M$ are consecutive even integers. Then possible length$(s)$ of the side$(s)$ of the triangle is (are)
$(A)$ $16$ $(B)$ $18$ $(C)$ $24$ $(D)$ $22$
In a triangle $P Q R, P$ is the largest angle and $\cos P=\frac{1}{3}$. Further the incircle of the triangle touches the sides $P Q, Q R$ and $R P$ at $N, L$ and $M$ respectively, such that the lengths of $P N, Q L$ and $R M$ are consecutive even integers. Then possible length$(s)$ of the side$(s)$ of the triangle is (are)
$(A)$ $16$ $(B)$ $18$ $(C)$ $24$ $(D)$ $22$
- [IIT 2013]
- A
$(A,D)$
- B
$(B,D)$
- C
$(B,C)$
- D
$(A,C)$
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