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

The distance from a point to a chord is a perpendicular (let’s call it OE). From the center of the circle to the ends of the chord, draw segments (OS and OB), which are radii. T. about. we got an isosceles triangle, in which OE is the height and median. Consider a right-angled triangle OEC: OE = 27, EC = 0.5 * CB = 36. The square of the hypotenuse CO ^ 2 = CE ^ 2 + OE ^ 2 = 1296 + 729 = 2025. Then CO = 45. The diameter is equal to two radii, m e. 90.
Answer: 90.