Circles

Let the radius of the circle be units. The area of the circle is given by the formula . The circumference of the circle is given by the formula . According to the problem, the area of the circle is numerically equal to its circumference. Therefore, we have the equation: $ , we can divide both sides of the equation by (assuming ): \) is twice the radius: \) $ Therefore, the diameter of the circle is 4 units.

Let the radii of the bigger and smaller circles be and respectively. Given: - Sum of diameters: cm, where implies . - Difference of radii: . Solving the system: Adding both: Subtracting: The area of a circle is proportional to the square of its radius. Hence,