Question

If the radius of the circle passing through the origin and touching the line $x+y=2$ at $\left(1,1\right)$ is $r$ units, then the value of $3\sqrt{2}r$ is

Answer 1

Answer: 3

Family of circles touching the given line at the given point is
${\left(x-1\right)}^2+{\left(y-1\right)}^2+\lambda \left(x+y-2\right)=0$
It passes through $\left(0,0\right)$ , hence $2-2\lambda =0\Rightarrow \lambda =1$
So, the equation of the circle is
$x^2+y^2-x-y=0$
Radius $=\frac{1}{\sqrt{2}}$