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.

Since the diameter of the circle is the base of an isosceles triangle, the height drawn from the apex of the triangle will be equal to the radius of the circle.

The diameter is equal to two radii.

Let us express the area of the triangle: Str = 1/2 * R * 2R = R².

Since the area of the triangle is 25 cm², then R² = 25, R = 5 cm.

Let’s calculate the circumference:

L = 2pR = 2 * p * 5 = 10p (cm).

Let’s calculate the area of a circle:

Scr = nR² = n * 5² = 25p (cm²).

Answer: the circumference is 10 cm, and the area of the circle is 25 cm ².