Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origin if $R$ is equal to

• A

  $\frac{1}{2}$
• Correct answer
  B

  $\frac{1}{\sqrt{2}}$
• C

  $\frac{1}{\sqrt{3}}$
• D

  $\frac{1}{3}$

Solution

$\begin{aligned} & \left(x-\frac{1}{2}\right)^2+\left(y-\frac{1}{2}\right)^2=R^2 \\ & \Rightarrow R^2=\frac{1}{2} ; R=\frac{1}{\sqrt{2}}\end{aligned}$

Hence, the correct answer is option: 'B'.