2. Solved Papers
  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2007

  • question_answer
    In a triangle, let\[\angle C=\pi /2\]. If r is the radius of incircle and R is the radius of circumcircle, then value of\[2(r+R)\]is

    A)  \[b+c\]             

    B)  \[a+b\]

    C)  \[a+b+c\]          

    D)  \[c+a\]

    Correct Answer: B

    Solution :

     \[\angle C=\frac{\pi }{2},\]we know that\[\frac{c}{\sin C}=2R\] \[\Rightarrow \]         \[c=2R\]            \[\left[ \because \sin \frac{\pi }{2}=1 \right]\] and   \[\tan \frac{C}{2}=\frac{r}{s-c}\] \[\Rightarrow \] \[\tan \frac{\pi }{4}=\frac{r}{s-c}\] \[\Rightarrow \] \[r=s-c=\frac{a+b+c}{2}-c\] \[\Rightarrow \] \[2r=a+b-c\] Now,    \[2r+27R=a+b-c+c\] \[\Rightarrow \] \[2(r+R)=a+b\]


You need to login to perform this action.
You will be redirected in 3 sec spinner