Arrangement of "circle" knowledge points in the second volume of ninth grade mathematics
Chapter 10 Circle
★ Key points ① Important properties of the circle; (2) the positional relationship between straight lines and circles, and between circles; ③ Angle theorem related to circle; ④ Theorem of proportional line segment related to circle.
☆ Summary ☆
First, the basic properties of the circle
Definition of 1. circle (two kinds)
2. Related concepts: chord and diameter; Arc, equal arc, upper arc, lower arc, semicircle; Distance from chord to center; Equal circle, same circle, concentric circle.
3. "Three-point circle" theorem
4. Vertical Diameter Theorem and Its Inference
5. "Equivalence" theorem and its inference
5. Angle related to circle: (1) Definition of central angle (equivalence theorem)
(2) the definition of the angle of circle (the theorem of the angle of circle, the relationship with the angle of center)
⑶ Definition of chord angle (chord angle theorem)
Second, the positional relationship between a straight line and a circle
1. Three positions and their judgments and properties:
Review outline of junior high school mathematics
2. The nature of the tangent (key point)
3. Judgment theorem of tangent (key point). What is the determination of the tangent of the circle (1)? ⑵?
4. Tangent length theorem
Third, the position relationship between circles.
Review outline of junior high school mathematics 1. Five positional relationships and their judgments and properties: (emphasis: tangency)
2. The property theorem of the tangent (intersection line) connecting two circles.
3. Common tangent of two circles: (1) Definition (2) Property
Four, proportional line segment related to the circle
Review outline of junior high school mathematics 1. the intersection string theorem
2. Cutting line theorem
Verb (abbreviation for verb) and regular polygon
The inscribed and circumscribed polygons of 1. circle (triangle, quadrilateral)
2. The circumscribed circle, inscribed circle and properties of triangle.
3. The properties of circumscribed quadrangles and inscribed quadrangles of a circle
4. Regular polygon and its calculation
Central corner: review outline of junior high school mathematics
Half of the Inner Corner: Review Outline of Junior High School Mathematics (right)
(Solve Rt△OAM to find out the relevant elements, junior high school mathematics review outline, junior high school mathematics review outline, etc. )
Six, a set of calculation formulas
1. circumference formula
2. Formula of circular area
3. Sector area formula
Review outline of junior high school mathematics 4. Arc length formula
5. Calculation method of arch area
6. The side development diagram of cylinder and cone and related calculation.
Seven, the trajectory of the point
Six basic trajectories
Eight, drawings.
1. Draw the circumscribed circle and inscribed circle of the triangle.
2. Divide known arcs equally
3. Find the median ratio of two known line segments.
4. Equal circumference: 4, 8; 6, 3 equal parts
Nine, the basic graphics
Important auxiliary line
1. Production radius
2. Chords are usually regarded as the distance from the center of the chord.
3. See the diameter is usually used as the circumferential angle on the diameter.
4. Don't forget to connect the center of the tangent point
5. Common tangent of two circles (connecting line)
6. Two circles intersect a common chord.