A circle touches x-axis at (2,0) and also the line $y=x$ in first quadrant then its radius is   

Centre   =  (2,k)   (say)

Cp = $\sqrt{0+k^2}=k$

                                     V = d                                                            x = y

$K=\left| \right|\left|\frac{1\left(2\right)-1\left(k\right)}{\sqrt{2}}\right|x-y=0$

$\sqrt{2}K=\left|-K+2\right|$

$\sqrt{2}K=2-K$

$(\sqrt{2}+1)K=2$     $K=\frac{2}{\sqrt{2}+1}$

$K=2(\sqrt{2}-1)$