Let ABCD be a trapezoid with the measure of base AB twice that of base DC, and let E be the point of intersection of the diagonals. If the measure of diagonal AC is 11, then what is the measure of segment EC?
We know AC = 11; we want EC = x.
Extend AD and BC to meet at F, forming △AFB.
Because △FDC ∼ △FAB and AB = 2DC, we know
FA = 2FD and FD = DA. Also FC = CB.
Thus AC and BD are medians, intersecting each other in the ratio 2:1.
So y + x = 11, y = 2x, 2x + x = 11, x = 11/3.
The answer is (a).