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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.