An isosceles triangle inscribed in a circle and its base is the diameter of the circle.

An isosceles triangle inscribed in a circle and its base is the diameter of the circle. Find the circumference and area of the circle if the area of the triangle is 25 cm ^ 2.

The area of the triangle is determined by the formula: S = 1 / 2h * a, where h is the height a is the base, from the condition of the problem: h = r, a = 2 * r where r is the radius. Then we get:
S = 1/2 * 2r * r = r *
r = √s = √25 = 5cm.
The circumference is equal to:
L = 2πr = 2 * 3.14 * 5 = 31.4 cm
The area of the circle is:
S = πr ^ 2 = 3.14 * 25 = 78.5cm ^ 2.