The mid-points of sides AB and AC of a triangle ABC are

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

1. 2 units
2. 6 units
3. 8 units
4. 4 units

Correct Option: D

As per the given in question , we draw a figure triangle ABC in which X and Y are the mid-points of sides AB and AC ,

Point X is the mid-point of AB. Point Y is the mid-Point of AC.
∴ XY || BC
∠AXY = ∠ABC
∠AYX = ∠ACB
By AA–similarity,
∆AXY ~ ∆ABC

∴	AX	=	XY
	AB		BC

⇒	AX	=	XY	⇒	BC	= 2
	2AX		BC		XY

By componendo and dividendo,

	BC + XY	=	2 + 1
	BC - XY		2 - 1

⇒	12	= 3
	BC -XY

⇒ BC – XY =	12	= 4 units.
	3