First, the definition of circle.

1, a graph composed of points with a fixed point as the center and a fixed length as the radius.

2. A graph composed of points with the same distance to a vertex on the same plane.

Second, the elements of the circle.

1, radius: the line connecting a point on a circle with the center of the circle.

2. Diameter: Two points on the connecting circle have a line segment passing through the center of the circle.

3. Chord: a line segment connecting two points on a circle (the diameter is also a chord).

Arc: A curve between two points on a circle.

4. A semicircle is also an arc.

(1) Bad arc: the arc is less than half a circle.

(2) Optimal arc: an arc larger than half a circle.

5. Central angle: an edge with the center of the circle as the vertex and the radius as the angle.

Supplementary content: III. Basic properties of a circle. 1, the symmetry of the circle. The (1) circle is an axisymmetric figure, and its symmetry axis is the straight line where the diameter lies. (2) A circle is a figure with a symmetrical center, and its symmetrical center is the center of the circle. (3) A circle is a rotationally symmetric figure. 2. Vertical diameter theorem. (1) bisects the chord perpendicular to its diameter and bisects the two arcs opposite the chord. (2) Inference: bisect the diameter (non-diameter) of the chord, perpendicular to the chord, and bisect the two arcs opposite the chord. Bisect the diameter of the arc and bisect the chord of the arc vertically. 3. The degree of the central angle is equal to the degree of the arc it faces. The degree of the circle angle is equal to half the radian it subtends. (1) The circumferential angles of the same arc are equal. (2) The circumferential angle of the diameter is a right angle; The angle of a circle is a right angle, and the chord it subtends is a diameter. 4. In the same circle or equal circle, as long as one of the five pairs of quantities, namely two chords, two arcs, two circumferential angles, two central angles and the distance between the centers of two chords, is equal, the other four pairs are also equal. 5. The two arcs sandwiched between parallel lines are equal. 6. Let the radius of ⊙O be r, and OP = d ... 7. (1) The center of the circle passing through two points must be on the vertical line connecting the two points. (2) Three points that are not on the same straight line determine a circle, the center of which is the intersection of the perpendicular lines of three sides, and the distances from this point to these three points are equal. The outer center of a right triangle is the midpoint of the hypotenuse.

6. Circumferential angle: the vertex is on the circumference, and the two sides of the circumferential angle are chords. 7. Chord center distance: the length from the center of the chord to the vertical section of the chord.