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1 Answer
- mizooLv 74 years agoFavorite Answer
the diagonal of the square = diameter of the larger circle
= √(10^2 + 10^2) = √200 = 10√2 cm
radius of the larger circle: 10√2/2 = 5√2
Area of the inner circle: pi * (5√2)^2 = 50pi
radius of the smaller circle: 10/2 = 5
Area of the smaller circle: pi * 5^2 = 25pi
The difference of two circles: 50pi - 25pi = 25pi : Area of the smaller circle
Using r for the radius of larger circle and R for the radius of smaller circle to prove it for any circle:
r = √(R^2 + R2) = R√2
Area of smaller circle: A1 = pi R^2
Area of larger circle: A2 = pi r^2 = pi (R√2)^2 = 2pi R^2
A2 - A1 = 2pi R^2 - pi R^2 = A1
