A square is inscribed in a circle of diameter 2a and another square is circumscribing circle. The difference between the areas of outer and inner squares is:
To find the difference between the areas of the outer square and the inner square, you can use the following approach:
Let the side length of the inner square be "x," and the side length of the outer square be "y." Since the inner square is inscribed in the circle, its diagonal is equal to the diameter of the circle, which is 2a. Using the Pythagorean theorem, we can relate x and the radius (a) of the circle:
x^2 + x^2 = (2a)^2 2x^2 = 4a^2 x^2 = 2a^2 x = a√2
Now, the side length of the outer square (y) is equal to the diameter of the circle, which is 2a:
y = 2a
To find the difference in their areas:
Area of outer square - Area of inner square = y^2 - x^2
Substitute the values of y and x:
(2a)^2 - (a√2)^2 = 4a^2 - 2a^2 = 2a^2
So, the difference between the areas of the outer square and the inner square is 2a^2.
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