Question

# In any equilateral Δ, three circles of radii one are touching to the sides given as in the figure then area of the Δ

Hint:

### In this question, we have to find the area of the triangle , This is equilateral triangle and three circles of radii one are touching to sides of the given figure. Here find the one side of triangle and apply the formula of the area of the equilateral triangle which is x side2.

## The correct answer is:

### Here, we have to find the area of the equilateral triangle.

Firstly, we have given equilateral triangle, ABC, in fig,

Here three circle inside the triangle, and their radii is 1 and center PQR, so we can write,

QD = 1, RE = 1, PF = 1.

∠ACB = 60° ( angle of equilateral triangle)

∠QCD = 30° ( intersection of angle ACB)

So ,tan 30° =

= [ since tan 30° = and QD = 1]

CD =

Similarly, EB =

DE = QR = 1 +1= 2

So, CB = CD + DE + EB

CB = ++

CB = 2 + = 2(1+ )unit

CB is side of triangle,

Since, the area of triangle,

Area = x side^{2}

= x (2(1+))^{2}

= x 4 ( 1 + )^{2}

= x ( 1 + 3 + )

= + + 2 x 3

= + 6 unit

Therefore, the correct answer is 6+

In this question, we have to find the area of the triangle, The formula of area of equilateral triangle is x side2. Find the length of one side of the triangle in which you have three circle is given with radius 1 unit.

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