$27 \cdot 3$ If $5x + 12y = 60$, then the minimum value of $\sqrt{x^2 + y^2}$ is
(A) $\frac{60}{13}$.
(B) $\frac{13}{5}$.
(C) $\frac{13}{12}$.
(D) 1 .
(E) 0 .
(12th American High School Mathematics Examination, 1961)
[Solution] Since $\sqrt{x^{2}+y^{2}}$ is the distance from the origin $O$ to the point $(x, y)$, finding the minimum value of $\sqrt{x^{2}+y^{2}}$ under the constraint (condition) $5 x + 12 y = 60$ is equivalent to finding the length of the perpendicular segment from $O$ to the line $5 x + 12 y = 60$.
By the similarity of right triangles $\triangle O C B \sim \triangle A O B$, we have
$$
\frac{O C}{O A}=\frac{O B}{A B} \text {, }
$$

then $O C=\frac{O A \cdot O B}{A B}=\frac{5 \cdot 12}{\sqrt{5^{2}+12^{2}}}=\frac{60}{13}$.
Therefore, the answer is $(A)$.