5. Choose $(x, y)$ in the coordinate plane so that its distances to the $x$-axis, $y$-axis, and the line $x+y=2$ are all equal, then the value of $x$ is
(A) $\sqrt{2}+2$,
(B) $2-\sqrt{2}$,
(C) $\sqrt{2}$,
(D) Not unique.
The above $(A),(B),(C)$ all fit when substituted into the problem, but according to the geometric characteristics, the incenter and the three excenters of the triangle formed by the $x$-axis, $y$-axis, and $x+y=2$ all fit the problem, so (D) should be selected.