A diameter is a cord in a circle containing the center of the circle. But some circles are sections of spheres. Not all diameters are diameters of spheres.
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There are an infinite number of diameters to any circle...
All diameters pass through the centre of a circle, is true.
An infinite number are possible, all in the same circle. If someone draws two diameters, then no matter how close together they are, you can come along and draw another one in between them. So there's no limit to the number.
False. The statement was fine until it reached the last requirement. Chords both pass through the center of the circle are diameters. If two of them shared one end point, they would also share the other end point. They would be the same diameter, and the angle between them would be zero.
That means that a given circle doesn't have two or three diameters. For a given circle, there is a unique measurement, called its "diameter". It is the distance from one end to the other, passing through the center. Since the circle is defined as all the points that are at the same distance from a point (the center), all radii are the same distance; and the diameter is simply twice the radius.