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Q: Is the center of a great circle also the center of a small circle?

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If talking in terms of the shortest distance around a sphere, the answer is NO.

A "great circle" is any circle on a sphere whose center is also the center of the sphere. The shortest distance between two points on the surface of a sphere is a piece of the great circle on which both points lie. A "small circle" is any circle on the sphere that's not a 'great' circle.

A diameter of a circle must pass through the center of that circle. A cord is a line segment that has its endpoints on the circumference of a circle. It can be any line segment. If that cord also passes through the center of the circle, it is said to be a diameter of that circle. A diameter of a circle is the longest cord of the circle.

Yes because the diameter of a circle is its largest chord passing through the center of the circle.

A radius of a circle is a line segment joining the center of the circle to a point on the circle. All such segments have the same length, and this length also called the radius of the circle.

Yes, a cord that is a diameter always passes through the center of a circle. And it's also the longest cord of that circle.

If you mean "what is the radius of a circle", then the answer is the line segment or length from the center of circle to the set of points that form the circle. The radius is also half of the diameter.

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 equator is a great circle. Meridians of longitude that cross over the north and south poles are also great circles. For every location on a great circle, it's antipodal location is also on the circle. Other than the equator itself, any great circle crosses the equator at two antipodal locations, 180° apart. Other than the equator and meridians of longitude that run due north and south, any great circle reaches it's maximum latitudes at two locations that are 90° of longitude east and west of the two locations where the great circle crosses the equator.Yes, since the intersecting plane that hypothetically forms the equator would cut through the center of the sphere.

Sure. Any chord that passes through the center of the circle is also a diameter. Chords can have many different lengths, but a diameter is the longest chord.

The diameter is the chord (line that goes from the circle to the circle) that goes through the center of the circle. It is the largest chord. It is also equal to twice the radius.

assuming this is a regular pentagon (all five sides are equal length) the center is the intersection of the intersection of perpendicular bisectors of each side and should also be the center of the circle in which it is inscribed

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