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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Properties of Triangles

JEE Main 2005 · Mathematics · Properties of Triangles

In a triangle ABC , let C=(π)/(2) . If r is the inradius and R is...

In a triangle ABC\mathrm{ABC}, let ∠C=π2\angle \mathrm{C}=\frac{\pi}{2}. If r\mathrm{r} is the inradius and R\mathrm{R} is the circumradius of the the triangle ABCA B C, then 2(r+R)2(r+R) equals

Options

  1. Ab+cb+c
  2. Ba+ba+b
  3. Ca+b+ca+b+c
  4. Dc+ac + a

Correct answer

B. a+ba+b

Step-by-step solution

2 r+2 R=c+2ab(a+b+c)=(a+b)2+c(a+b)(a+b+c)=\frac{2 a b}{(a+b+c)}=\frac{(a+b)^2+c(a+b)}{(a+b+c)}=a+b \quad\left(\text{ since })$c^2=a²+b²\right)
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