$20 \cdot 52$ A side of a triangle is divided by the point of tangency of its inscribed circle into segments of 6 units and 8 units, respectively. If the radius of this circle is 4 units, then the length of the shortest side of this triangle is 
(A) 12 units.
(B) 13 units.
(C) 14 units.
(D) 15 units.
(E) 16 units.
(4th American High School Mathematics Examination, 1953)
[Solution] Let the three sides of the triangle be $a, b, c$, the semi-perimeter be $p$, and the inradius be $r$, then
$$
r=\sqrt{\frac{(p-a)(p-b)(p-c)}{p}},
$$

Given $4=\sqrt{\frac{6 \cdot 8 \cdot x}{6+8+x}}$, solving for $x$ yields $x=7$.
Thus, the smallest side of the triangle is 13.
Therefore, the answer is (B).