A chord is drawn in the circle, the length of which is 8 cm and is 3 cm away from the center. Find the diameter of the circle.

The distance from the center of the circle to the chord is equal to the length of the perpendicular dropped from the center to the chord. Connecting the center to the ends of the chord, we get an isosceles triangle, whose base is equal to the chord, and the sides are equal to the radius R. The perpendicular from the center will be the height of the isosceles triangle and will divide the chord in half.
Consider a triangle formed by a perpendicular h = 3 cm, half a chord a = 8/2 = 4 cm, and a radius R.
The triangle is rectangular, so the radius R according to the Pythagorean theorem is:
R ^ 2 = h ^ 2 + a ^ 2 = 3 ^ 2 + 4 ^ 2 = 25 cm ^ 2;
R = √25 = 5 cm.
Diameter D = 2R = 2 * 5 = 10 cm.
Answer: 10 cm.