What are the summary of the knowledge points of mathematics circle in the third year of junior high

Summary of the knowledge points of the third year of junior high school mathematics circle:

1. Definition of a circle.

1) In a plane, the shape formed by the rotation of the line segment oa around one of its endpoints o and the rotation of the other endpoint a is called a circle. The fixed endpoint o is called the center of the circle, and the line segment oa is called the radius.

2) A circle can be seen as a set of points whose distance from the plane to the fixed point is equal to the fixed length, the fixed point is the center of the circle, and the fixed length is the radius of the circle.

Note: The position of the circle is determined by the center of the circle, the size of the circle is determined by the radius, and two circles with equal radius are equal circles.

2. The concept of circle.

1) String: A line segment that connects any two points on a circle.

2) Diameter: The string that passes through the center of the circle. The diameter is equal to 2 times the radius.

3) Arc: The part between any two points on a circle is called an arc. Among them, the arc larger than the semicircle is called the superior arc, such as CAD, and the arc smaller than the semicircle is called the inferior arc.

4) Center Angle: As shown in the figure on the right, COD is the center angle.

3. The relationship between the central angle, arc, chord, and chord centroid distance.

1) Theorem: In the same circle or equal circle, the arcs of the opposite central angles of the equal circles are equal, and the chord centroid distances of the paired strings are equal.

2) Corollary: In the same circle or equal circle, if one set of quantities is equal in the central distance of two circles, two arcs, two strings, or two strings, then the rest of the groups of quantities corresponding to them are equal.

4. A circle of three points.

1) Theorem: Three points that are not on the same straight line determine a circle.

2) The circumscribed center of the triangle (outer center) is the intersection of the three perpendicular bisectors.

5. Perpendicular diameter theorem.

Bisect the string perpendicular to the diameter of the string, and bisect the two arcs opposite the string. Corollary:

1) The diameter of the bisector chord (not the diameter) is perpendicular to the chord, and the two arcs opposite the bisecting chord.

The perpendicular bisector of the string passes through the center of the circle and bisects the two arcs opposite the chord.

The diameter of one string to which the bisector string is paired, the perpendicular bisector of the chord, and the other arc to which the bisector chord is paired.

2) The arcs sandwiched by the two parallel chords of the circle are equal.

Students who are about to enter the third year of junior high school should master the knowledge content about circles, which will be helpful for the later contact with arcs, fans, ellipses and other related knowledge content. The following is a summary of the circle knowledge points of junior high school mathematics that I have compiled for your reference.

Definition: 1) A figure composed of all points on a plane whose distance from the fixed point to the fixed point is equal to that of a fixed length is called a circle.

2) A line segment on a plane rotates 360° around one end of it, leaving a trajectory called a circle.

Center of the circle: 1) As in definition (1), the fixed point is the center of the circle.

2) As defined (Tong Trace 2), the endpoint of the winding end is the center of the circle.

3) The intersection point of any two axes of symmetry of the circle is the center of the circle.

4) The binonox of a line segment perpendicular to any chord in the circle and with two endpoints on the circle is the center of the circle.

Note: The center of the circle is generally represented by the letter O.

1.The positional relationship between points and circles.

The point is in the circle< = > the distance from the point to the center of the circle is less than the radius;

Point on a circle< = > distance from the point to the center of the circle is equal to the radius;

Point outside the circle< = > distance from the point to the center of the circle is greater than the radius.

2.A circle that crosses three points that are not three points on the same line determines a circle.

3.The circumscribed circle and the outer center pass through the three vertices of the triangle to make a circle, and this circle is called the circumscribed circle of the triangle. The center of the circumscribed circle is the sensitive point where the three sides of the triangle cross the perpendicular bisector, which is called the outer center of the triangle.

4.The positional relationship between a line and a circle.

Intersection: A straight line and a circle have two common points called the line intersecting the circle, and this line is called the secant of the circle.

Tangent: A line and a circle have a common point called the line tangent to the circle, this line is called the tangent of the circle, and this point is called the tangent point.

Separation: A line and a circle do not have a common point, which means that the line and the circle are separated.

5.The nature and determination of the positional relationship between a line and a circle.

If the radius of o is r, and the distance from the center of the circle o to the line l is d, then.

The straight line l intersects with the local skin and o<=>d<>;

The straight line l and o are tangent<=>d=r;

The straight lines l and o are separated by <=>d>r.

1.The circumference of the circle c=2 r= d.

2.The area of the circle s=s= r2.

3.The arc length of the sector l=n r 180.

4.Sector area s=n r2 360=rl 2.

5.The area of the conical side is = rl.

The knowledge points of the junior high school math circle are as follows:1. The symmetry of the circle, although some other graphs also have it, but the circle has an infinite number of symmetry axes This characteristic is not found in other graphs, the vertical diameter theorem, the tangent length theorem, and the calculation of regular n-sided shapes are all applied to this characteristic.

2. A circle can be seen as a set of points whose distance to a fixed point is equal to a fixed length.

3. Circle: The trajectory of the point where the distance to the fixed point is equal to the fixed length is the circle with the fixed point as the center and the fixed length as the radius.

4. Pi is a constant, which represents the ratio of circumference and diameter. It is an irrational number, i.e. an infinite non-cyclic decimal.

5. The circumference of the circle: The length of the curve that encloses the circle is called the circumference of the circle, which is represented by the letter C.