The chord length of the circle is 72, and the distance from the center to the circumference of this chord is 27

The chord length of the circle is 72, and the distance from the center to the circumference of this chord is 27. Find the diameter of the circle.

To solve this problem, we will use the property that a straight line drawn from the center of the circle to the center of the chord will divide the chord in half.
And together with the radius, these three segments form a right-angled triangle, the legs of which are 27 and 72/2 = 36.
Therefore, the radius will be equal to the length of the hypotenuse of this rectangle.
Then, we get a radius equal to the square root of the sum 27×27 + 36×36 = 45.
Therefore, the diameter of the circle will be equal to two radii 45 + 45 = 90.
Answer: the diameter of the circle is 90.