Question

In a right-angled isosceles triangle, the ratio of the circumradius and inradius is

• A. $2(\sqrt{2}+1):1$
• B. $(\sqrt{2}+1);1$
• C. $2:1$
• D. $\sqrt{2}1$

Answer 1

The correct option is B $(\sqrt{2}+1);1$

Let the two equal sides of the right angled isosceles triangle be a, then
Circumcentre = $\frac{1}{2}a\sqrt{2}$
Incentre = $a(1-\frac{1}{2}\sqrt{2})$
Required ratio = $\frac{\frac{1}{2}a\sqrt{2}}{a(1-\frac{1}{2}\sqrt{2})}$

= $\frac{\sqrt{2}}{2-\sqrt{2}}=\frac{\sqrt{2}+1}{1}$
Hence, the correct option is 'B'.