The inner circle is the largest one that can be drawn inside the square. The outer circle is the smallest one that can be drawn with the square inside it. Prove that the shaded area between the 2 circles is the same as the area enclosed by inner circle?
1 Answer
Oct 14, 2017
If we call the radius of the smaller circle
The diameter of the larger circle is given by pythagoras, because it can be found by drawing a diagonal through the square.
R^2 = 10^2 + 10^2 = 200R2=102+102=200
R = sqrt(200) = sqrt(100 * 2) = 10sqrt(2)R=√200=√100⋅2=10√2
Then the area of the larger circle is
Because the area of the inner circle is
50pi - 25pi = 25pi50π−25π=25π
Or the same as the inner circle.
So we've proved that this is the case.
Hopefully this helps!