Question

a circle is inscribed in an equilateral triangle of side root 3 units which of the following is the area of the square constructed with the diameter of the circle as a side in square units​

Answer 1

ANSWER

Clearly, centre of triangle , circle and square coincides. (Centroid, incenter of equilateral triangle , orthocenter coincides)

Let a be the length of side of an equilateral triangle.

Area of equilateral triangle A1=43a2

We have radius of inscribed circle r=23a×31=23a

So, diameter= 3a

We know that the diameter of the inscribed circle is equal to the diagonal of the square.

So, diagonal of square =3a

Let x be the length of side of square.

Length of diagonal of square =x2

x2=3a

⇒x=6a

Area of square A2=x2=6a2

Now,A2A1=6a243a2

⇒A2A1=233

hope this will help u