The mid points of AB and AC of a triangle ABC are respectively X & Y. If BC + XY = 12 units, then the value of BC - XY is:

Given : X and Y are mid points of AB and AC respectively of triangle ABC and BC + XY = 12 units ---------(i)

=> $$\frac{AX}{AB}=\frac{AY}{AC}=\frac{XY}{BC}=\frac{1}{2}$$ -------------(ii)

To find : BC - XY = ?

Solution : From equation (ii), let BC = $$2z$$ and $$XY=z$$

Substituting it in equation (i), => $$2z+z=3z=12$$

=> $$z=\frac{12}{3}=4$$ units

=> BC = 8 units and AX = 4 units

$$\therefore$$ BC - XY = 8-4 = 4 units

=> Ans - (D)