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**Construction of a circle**

The circle is the set of all points of the plane which have the same distance r from a fixed point M of the plane.

M is called the center, and the distance of length r connecting each point of the circle to its center is called the radius. According to this definition - domyhomework.club , the circle is a line, the circle line. The center point M does not belong to the circle according to this definition.

All boundary points and all inner points of a circle together form the area of the circle, the circular area. From the context it is usually clear whether the word "circle" means the circle line or the circle area.

A point is called with respect to a circle with center M and radius r:

- inner point Q if QM (average) < r,

- boundary point P, if PM (average) = r and

- outer point R, if RM (average) > r

Exactly one circle can always be drawn through three points not lying on a straight line - https://domyhomework.club/math-problem-solver/ . Its center is the intersection of the perpendiculars of the connecting lines of the three points. If two circles have three points in common, the circles are identical.

**Circle and symmetry**

Every circle is axisymmetric. Every straight line through the center of the circle is an axis of symmetry, thus a circle has infinitely many axes of symmetry - https://domyhomework.club/geometry-homework/ . Every circle is point and rotation symmetric with its center as the center of symmetry and rotation.

If for two circles M1=M2 and r1 ≠ r2 holds, the circles are called concentric circles. The area between two concentric circles is called a circular ring.

**More information:**

Basic information about motion

Rene Descartes: Origin and education