In the given figure, D, E and F are the midpoints of the sides BC, CA and AB of `DeltaABC. BE` bisect DF at X while CF bisect DE at Y, then BC = a XY. Find a.

Explanation

In `triangle ABC`, F and E are the midpoints of AB and AC respective
`therefore " FE||BC and "FE=(1)/(2)BC=BD.`
`therefore " FE||BD and "FE = BD.`
So, BDEF is a parallelogram whose diagonals BE and DF intersect each other at X.
`therefore ` X is the midpoint of DF.
Similarly, Y is the midpoint of DE.
Thus, in `triangle DEF`, X and Y are the midpoints of DF and DE respectively.
So, XY||FE and `XY = (1)/(2)FE =(1)/(2)xx(1)/(2)BC=(1)/(4)BC.`