Find the circumference and area of a circle if AB is the diameter of the circle and the chords AC

Find the circumference and area of a circle if AB is the diameter of the circle and the chords AC and BC are 12 cm and 9 cm

A triangle based on a diameter is always rectangular. Therefore, triangle ABC is rectangular, AC and BC are legs, AB is hypotenuse, equal to the diameter of the circumscribed circle. The sum of the squares of the legs is equal to the square of the hypotenuse, therefore: AB ^ 2 = AC ^ 2 + BC ^ 2 = 12 ^ 2 + 9 ^ 2 = 144 + 81 = 225; AB = √225 = 15 cm. Knowing the diameter, we find the circumference: l = πD = π * 15≈ 47.12 cm. The area of the circle is S = π (D ^ 2) / 4 = π * (15 ^ 2) / 4 = π * 225 / 4≈ 176.71 cm.