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Q: How do you find a point which is equidistant from other three points?

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It is the circumcentre of the triangle formed by the three points. Draw the perpendicular bisectors of two of the lines joining the three points. They will meet at the point that is equidistant from the three points.

circumcenter

It is the point known as the incentre.

No, a sphere and a circle are different geometric shapes. A sphere is a three-dimensional object with all points equidistant from the center, while a circle is a two-dimensional shape with all points equidistant from the center. In other words, a circle is a flat, circular shape, while a sphere is a three-dimensional, round object.

It depends on how many dimensions you are asking about. If you are talking about a 2-dimensional figure then it would be a circle. The definition of a circle is the collection of points that are equidistant from the center. If you are talking about a 3-dimensional figure, then it would be a sphere. The definition of a sphere is the collection of points in three dimensions that are equidistant from the center.

Related questions

To find a point equidistant from three other points, construct perpendicular bisectors for two of the segments formed from three points. Note: this will be the center of the circle that has all three points on it's circumference. Three points, not in a straight line, form three pairs of points with each pair defining a different line. Take any pair of points and draw the perpendicular bisector of the line joining them. Repeat for one of the other pairs. These two perpendicular bisectors will meet at the point which is equidistant from all three points - the circumcenter of the triangle formed by the three points.

Triangle

A 'spherical' surface.

It is the circumcentre of the triangle formed by the three points. Draw the perpendicular bisectors of two of the lines joining the three points. They will meet at the point that is equidistant from the three points.

The surface of a sphere is defined in that manner.

On a sphere, all points on the surface are equidistant from the center.

point K is equidistant from points L, M, and N

circumcenter

It is the point known as the incentre.

A three-dimentional shape at all points equidistant from a straight line.

No, a sphere and a circle are different geometric shapes. A sphere is a three-dimensional object with all points equidistant from the center, while a circle is a two-dimensional shape with all points equidistant from the center. In other words, a circle is a flat, circular shape, while a sphere is a three-dimensional, round object.

It depends on how many dimensions you are asking about. If you are talking about a 2-dimensional figure then it would be a circle. The definition of a circle is the collection of points that are equidistant from the center. If you are talking about a 3-dimensional figure, then it would be a sphere. The definition of a sphere is the collection of points in three dimensions that are equidistant from the center.