Question

Given a square with area A. A circle lies inside the square, such that the circle touches all sides of the square. Another square
with area B lies inside the circle, such that all its vertices lie on the circle.
Find the value of A/B​

Answer 1

Answer:

Let the area of Larger circle be 'r' and the area of smaller circle by 'r1'

In triangle ACR,

CR=r=AR (radius of the circle)

AC=CD+BD+AB

Now, CD=r

DB=r1

To find AB, we need to apply pythagoras theorem in triangle ABQ.

In triangle ABQ,

AQ=BQ=r1 (radius of the circle)

and AB=(2)r1

⇒AC=r+r1(1+(2))

Applying pythagoras theorem in triangle ACR,

2r2=(r+r1(1+(2)))2

solving, we get r=r1(3+2(2))------(1)

Sum of areas of all small circles = 4π(r1)2

Area of larger circle = π(r)2

Ratio of areas = 4π(r1)2πr2

Using equation (1), we get ratio of areas = 417+2(2)