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

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 $=\frac{1}{\sqrt{2}}$