$20 \cdot 106$ A belt is installed on two pulleys with radii of 14 inches and 4 inches (the belt is taut and does not cross), if the distance between the points of tangency on the two pulleys is 24 inches, then the distance between the centers of the two pulleys (in inches) is
(A) 24 .
(B) $2 \sqrt{119}$.
(C) 25 .
(D) 26 .
(E) $4 \sqrt{35}$.
(22nd American High School Mathematics Examination, 1971)
[Solution] As shown in the figure, a right triangle is formed by the line connecting the centers, a radius, and a line parallel to the belt, with the legs of the triangle being 24 inches and 10 inches.
Thus, $d$ satisfies $d^{2}=24^{2}+10^{2}=26^{2}$,
which means $d=26$ inches.
Therefore, the answer is $(D)$.