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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.

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

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The surface of a sphere is defined in that manner.

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

They must be collinear.

If three points all lie on the same line, then the points are said to be "collinear". This is also true if the slope from each point to the next is the same.

It takes 3 non collinear points to define one specific circle. With only two points an infinite number of circles can be drawn. Proof: Given two points A, B draw the line between them. Then find the perpendicular bisector of the line AB. Any point on the perpendicular bisector is equidistant from the two original points, A and B. A circle with center C and radius AC will then pass through points A and B. There are infinite point C's on the perpendicular bisector so there are infinite circles. Given three points A, B and D you can find the perpendicular bisector for line segements AB and then the perpendicular bisector fof line segment BC. The two perpedicular bisectors will not be parallel because the points A, B and D are non collinear. This means the two perpeniducar bisectors will intercept at only one point C(like any two intercepting lines). This point C is equidistant from points A, B, and D. A circle with center C and radius AC will then pass through all three of the points. Since there is only one point C that lies on both perpendicular bisectors, there is only one circle possible.

Related questions

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.

The point equidistant from the three sides of a triangle is the center of the triangle. The center of the triangle is the point of intersection of the medians of the triangle. The medians of a triangle are the line segments that join the vertices of the triangle to the midpoints of the opposite sides.