Question 22
(HUN 3) The distance between the centers of the circles $k_1$ and $k_2$ with radii $r$ is equal to $r$. Points $A$ and $B$ are on the circle $k_1$, symmetric with respect to the line connecting the centers of the circles. Point $P$ is an arbitrary point on $k_2$. Prove that $$PA^2+PB^2\ge2r^2.$$ When does equality hold?