A triangle is formed by the tangents at the point (2,2) on the curves y^2=2 x and x^2+y^2=4 x, and the line x+y+2=0. If r is the radius of its…

A triangle is formed by the tangents at the point $\displaystyle (2,2)$ on the curves $\displaystyle y^2=2 x$ and $\displaystyle x^2+y^2=4 x$, and the line $\displaystyle x+y+2=0$. If $\displaystyle r$ is the radius of its circumcircle, then $\displaystyle r^2$ is equal to $\displaystyle \_\_\_\_$.