Two Squares and a Circle - Problem With Solution

A problem, with detailed solution, on a circle inscribed in one square and circumscribed to another, is presented.

Problem

The small square is inscribed inside the circle and the larger circle circumsrcibes the same circle. If A1 is the area of the large square and A2 is the area of the small square, what is the ration A1 / A2?
two squares and one circle - problem

Solution to Problem :

  • If x is the size of one side of the small square, then its area A2 is given by
    A2 = x 2
    two squares and one circle - solution

  • The diagonal d of the small square is given by
    d 2 = x 2 + x 2
    d = x sqrt (2)
  • d is also equal to the side of one side of the large square
  • The area A1 of the large square A1 is given by.
    A1 = ( x sqrt (2) ) 2 = 2 x 2
  • Hence
    A1 / A2 = 2 x 2 / x 2 = 2

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