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Q: Does every great circle of a sphere have to pass through its center?

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No. Every circle on the sphere whose center is also the center of the sphere is a great circle. If the circle's center is not also the center of the sphere, then the circle is a small circle.

Sure.A circle is the shape of every possible CUT through a sphere with a flat knife.

A 'great circle' is any circle on the surface of a sphere that has its center at the center of the sphere. The equator is the only parallel of latitude that's a great circle. Every meridian of constant longitude is a semi-circle, and together with the one directly opposite it, they form a great circle. The shortest distance between two points on a sphere is the piece of the great circle through them.

Every cross-section of a sphere is a circle.

Every diameter of the circle.

... center of the circle.

It is the center of the circle

A circle has a round shape in which every point on the circle is the same distance from one point called "the center". The center of a circle is not on the circle.

No. The chord is a diameter only if it passes through the center of the circle. In that case,it's also the longest that any chord can possibly be in that circle.

The precise definition of the word 'centres' is the middle point of a circle or a sphere. This means the point is an equal distance from every point on the circle/sphere.

A sphere is a solid figure in which every point is equidistant from a fixed point called the center.

Every section of a solid sphere is a filled-in circle, i.e. a disk with zero thickness.

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