A circle is made inside an equilateral triangle and inside the circleA

1.	A circle is made inside an equilateral triangle and inside the circleA square is formed. The area of the triangle with the area of the squareThe ratio will be:
Answer» Step-by-step EXPLANATION: 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 A 1 = 4 3 a 2 We have radius of INSCRIBED circle r= 2 3 a× 3 1 = 2 3 a So, diameter= 3 a We know that the diameter of the inscribed circle is equal to the diagonal of the square. So, diagonal of square = 3 a Let x be the length of side of square. Length of diagonal of square =x 2 ⇒x 2 = 3 a ⇒x= 6 a Area of square A 2 =x 2 = 6 a 2 Now, A 2 A 1 = 6 a 2 4 3 a 2 ⇒ A 2 A 1 = 2 3 3

A circle is made inside an equilateral triangle and inside the circleA square is formed. The area of the triangle with the area of the squareThe ratio will be:

Answer»

Step-by-step EXPLANATION:

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 A

We have radius of INSCRIBED circle r=

a×

So, diameter=

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

So, diagonal of square =

Let x be the length of side of square.

Length of diagonal of square =x

⇒x

⇒x=

Area of square A

Now,

⇒