18.101 In trapezoid $A B C D$, one base $A B$ is twice the other base $D C$, and $E$ is the intersection of the two diagonals. If diagonal $A C$ is 11, then $E C$ is equal to
(A) $3 \frac{2}{3}$.
(B) $3 \frac{3}{4}$.
(C) 4 .
(D) $3 \frac{1}{2}$.
(E) 3 .
(23rd American High School Mathematics Examination, 1972)
[Solution] Let the sides $A D, B C$ intersect at $V$, then the diagonals $A C, B D$ are two medians of $\triangle A B V$, and their intersection point $E$ divides $A C$ in the ratio $2: 1$.
Therefore, the length of $E C$ is $\frac{11}{3}$ or $3 \frac{2}{3}$ units. Hence, the answer is $(A)$.