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*?

- 11/3
- 15/4
- 4
- 7/2
- 3

We know

*AC*= 11; we want*EC*=*x*.Extend

*AD*and*BC*to meet at*F*, forming △*AFB*.Because △

*FDC*∼ △*FAB*and*AB*= 2*DC*, we know*FA*= 2

*FD*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*= 2*x*, 2*x*+*x*= 11,*x*= 11/3.The answer is (a).