26-24 If $r$ is a positive number, and the line with equation $x+y=r$ is tangent to the circle with equation $x^{2}+y^{2}=r$, then $r$ equals
(A) $\frac{1}{2}$.
(B) 1 .
(C) 2 .
(D) $\sqrt{2}$.
(E) $2 \sqrt{2}$.
(29th American High School Mathematics Examination, 1978)
[Solution] If the line with the equation $x+y=r$ is tangent to the circle with the equation $x^{2}+y^{2}=r$, it is easy to find that the point of tangency is $\left(\frac{r}{2}, \frac{r}{2}\right)$, and the distance between this point and the origin is $\sqrt{r}$.
$\therefore\left(\frac{r}{2}\right)^{2}+\left(\frac{r}{2}\right)^{2}=r$, solving this gives $r=2$.
Therefore, the correct choice is $(C)$.