A rectangle with sides of 16 cm and 12 cm is inscribed in the circle. Find the area of the circle.

The circle touches the sides of the rectangle. The diagonal of the inscribed rectangle will be equal to the diameter of the circle, and since the diagonal divides the rectangle in half, we will get a right-angled triangle. Therefore, by the Pythagorean theorem, we find:
d ^ 2 = a ^ 2 + b ^ 2 = 16 ^ 2 + 12 ^ 2 = 400;
d = 20;
Find the radius:
R = d / 2 = 20/2 = 10;
Find the area of the circle:
S = PiR ^ 2;
S = Pi10 ^ 2 = 100Pi.
Answer: S circle = 100Pi.