Let AX⊥ BC of an equilateral triangle ABC. Then the

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Let AX⊥ BC of an equilateral triangle ABC. Then the sum of the perpendicular distances of the sides of ∆ABC from any point inside the triangle is :

1. Equal to BC
2. Equal to AX
3. Less than AX
4. Greater than AX

Correct Option: B

On the basis of given in question , we draw a figure of an equilateral triangle ABC ,

Let O be a point inside the triangle.
OD ⊥ BC, OE ⊥ AC and OF ⊥ AB
AB = BC = CA
Area of (∆ OAB + ∆OBC + ∆OAC) = Area of ∆ABC

⇒	1	× AB × OF +	1	× BC × OD +	1	× AC × OE
	2		2		2

Area of ∆ABC =	1	× BC × AX
	2

⇒ OF + OD + OE = AX