AHSME 1969 Problem 21

If the graph of $x^2+y^2=m$ is tangent to that of $x+y=\sqrt{2m}$, then: $\text{(A) m must equal } \tfrac{1}{2} \text{(B) m must equal } \frac{1}{\sqrt{2}} \\ \text{(C) m must equal } \sqrt{2} \text{(D) m must equal } 2 \\ \text{(E) m may be any non-negative real number}$