2. The angle of the vertex at the center of the circle is called the central angle. The distance from the center of the circle to the chord is called the chord center distance.
Circular Power Theorem (Intersection Theorem, Secant Theorem and Their Inference (Secant Theorem) are collectively called Circular Power Theorem)
Tangent length theorem
Vertical theorem
the circumferential angle theorem
Alternating line segment theorem
Four-circle theorem
3. In the same circle or in the same circle, the isocentric angle has equal arc, chord and chord center distance.
4. In the same circle or circle, if one of two central angles, two arcs, two chords or the distance between two chords is equal, their corresponding other components are equal respectively.
5. Divide the whole circumference into 360 equal parts, and each arc is an arc of 1. The degree of the central angle is equal to the degree of the arc it faces.
6. A circle is a figure with a symmetrical center, that is, it can overlap with the original figure after rotating180 around its symmetrical center (center). This attribute is not difficult to understand. Different from other centrosymmetric figures, the circle also has rotation invariance, that is, it can overlap the original figure by rotating it at any angle around its center.
7. Vertical diameter theorem
The diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord.
8.( 1) bisect the diameter of the chord (not the diameter) perpendicular to the chord and bisect the two arcs opposite the chord.
(2) The perpendicular line of the chord passes through the center of the circle and bisects the two arcs opposite to the chord.
(3) bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord.
9. The arcs between two parallel chords of a circle are equal.
10.( 1) An arc subtends a circumferential angle equal to half the central angle it subtends.
(2) The circumferential angles of the same arc or equal arc are equal; In the same circle or in the same circle, the arcs with equal circumferential angles are also equal.
(3) The circumference angle (or diameter) of a semicircle is a right angle; A chord with a circumferential angle of 90 is a diameter.
(4) If the median line of one side of a triangle is equal to half of this side, then this triangle is a right triangle.
1 1.( 1) A circle is an axisymmetric figure, and every straight line passing through the center of the circle is its axis of symmetry.
(2) The diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite to the chord.
(3) The diameter of bisecting the chord (not the diameter) is perpendicular to the chord and bisects the two arcs opposite the chord.
(4) The perpendicular bisector of a chord bisects two opposite chords through the center of the circle.
(5) bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord.
(6) The number of radians between two parallel chords of a circle is equal.
12. A circle is an axisymmetric figure, and every straight line passing through the center of the circle is its axis of symmetry.
The diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord.
13. bisect the diameter of the chord perpendicular to the chord (not the diameter) and bisect the two arcs opposite the chord.
14. In the same circle or circle, the isocentric angle has equal arc, chord and chord center distance.
15. In the same circle or equal circle, equal chords have the same arc, the same central angle and the same distance between the chords.
16. The same arc has countless relative circumferential angles.
17. The ratio of the arc is equal to the ratio of the central angle of the arc.
18. Diagonal complementation or equality of inscribed quadrangles of a circle.
19. Three points that are not on a straight line can determine a circle.
20. The diameter is the longest chord in a circle.
The 2 1. chord divides the circle into an upper arc and a lower arc.
3. 1 the positional relationship between two circles
Two circles that do not overlap on a plane. Their positional relationship has the following five situations: external separation, external tangency, intersection, internal tangency and external tangency.
A straight line passing through the centers of two circles is called the connecting line of two circles, and the distance between the centers is called the center distance.
theorem
The connecting line of two circles is the symmetry axis of two circles. When two circles are tangent, their tangents are all on the connecting line.
(1) Two circles are separated from each other.
d & gtR+r
(2) circumscribe two circles
d=R+r
(3) Two circles intersect
Right rear)
(4) Two circles are inscribed.
d=R-r
(R & gtr)
(5) Two circles contain
Doctor)
In special cases, two circles are concentric circles.
d=0
3.2 Common tangent of two circles
Memorize these theorems, and you don't have to worry ~
theorem
The appearance of two tangents of two circles, etc. The lengths of the two internal common tangents of two circles are also equal.