The length of a chord of a circle is 64, and the distance from the center of the circle

The length of a chord of a circle is 64, and the distance from the center of the circle to this chord is 60, you will find the diameter of the circle.

Let’s construct the radii of the circles OA, and OB to the ends of the chord AB. The AOB triangle is isosceles, since ОА = ОВ = R.

The OH segment is the height and median of the AOB triangle, then AH = BH = AB / 2 = 64/2 = 32 cm.

Since OH is the height, the triangles AOH and BOH are rectangular, then, by the Pythagorean theorem, we determine the length of the hypotenuse OA.

OA ^ 2 = AH ^ 2 + OH ^ 2 = 1024 + 3600 = 4624.

ОА = 68 cm.

Then R = OA = 68 cm, D = 2 * R = 2 * 68 = 136 cm.

Answer: The diameter of the circle is 136 cm.