1, the basic concept of a circle: A circle is a geometric figure and a closed curve formed by the rotation of a line segment around an endpoint. A circle has countless symmetry axes, and the symmetry axis is a straight line passing through the center of the circle.

2. The nature of the circle: the circle is an axisymmetric figure, and its symmetry axis is a straight line passing through the center of the circle; The circle has rotation invariance, that is, the shape and size of the circle will not change during rotation; A circle is a figure with a symmetrical center, that is, any angle that the circle rotates around its center will coincide with the original figure.

3. The circumference and area of a circle: the circumference of a circle refers to the length of a circle, which is expressed by the formula C=πd, where π is an irrational number, which is about equal to 3. 14 159, and d is the diameter of a circle; The area of a circle refers to the size of the plane occupied by the circle, using the formula S=πr? , where π is an irrational number, which is approximately equal to 3. 14 159, and r is the radius of the circle.

4. Relationship between a circle and a straight line: When a straight line intersects a circle, it will intersect at two points; When a straight line and a circle are tangent, they have only one common point; When a straight line and a circle are separated, they have nothing in common.

5. Equation of circle: In the plane rectangular coordinate system, the standard equation of a circle with point O(a, b) as the center and R as the radius is (x-a)? +(y-b)？ =r？ .