The legs of a right-angled triangle inscribed in a circle are equal to 3 cm and 40 cm. What is the diameter of the circle?

Since the legs of a right-angled triangle are inscribed in a circle, the value of the inscribed angle ABC is 90, then the degree measure of the arc on which it rests is 2 * 90 = 180.

Then the chord AC contracting this arc is the hypotenuse of the triangle and the diameter of the circle.

By the Pythagorean theorem, AC ^ 2 = D ^ 2 = AB ^ 2 + BC ^ 2 = 9 + 1600 = 1609.

AC = √1609 ≈ 40.11 cm

Answer: The diameter of the circle is 40.11 cm.