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Round. The diameter of a circle connects two ends (one end is on the circle and the other end is on the diameter).
This angle is a right angle.
This is called the vertical diameter theorem.
The theorem of circle angle is
Number; Amount; How much; number; amount; how many; how much
-Multiply the area or circumference of a circle = the area of this fan row or that arc.
360
I don't know the rest.
A circle is a central symmetrical figure with the center of the circle as the symmetrical center; Any rotation angle α around the center of the circle can coincide with the original.
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. The vertical diameter theorem bisects the chord perpendicular to its diameter and bisects the two arcs opposite to 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 equal arcs, equal central angles and equal chord center distances.
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.
Supplement: Nine-point * * * Circle Theorem
The midpoint of three sides of a triangle, three high vertical legs, and the midpoint of the line connecting the vertical center and each vertex are 9 * * * circles.
The nine-point circle is a famous problem in the history of geometry. It was first put forward by Benjamin Bevan of England. The question was published in the British magazine 1804. The first person who proved this theorem completely was the French mathematician Poncelet [1788- 1867]. Some people say that it was made by French mathematicians in 1820- 182 1 year. Feuerbach [1800- 1834], a high school teacher, also studied the nine-point circle. His proof was published in 1822' s paper "Some Special Points of Straight Triangle". In this paper, Feuerbach also obtained some important properties of the nine-point circle (such as the following property 3), so some people called the nine-point circle Feuerbach circle.
The nine-point circle has many interesting properties, such as:
1. The radius of the triangle nine-point circle is half of the radius of the triangle circumscribed circle;
2. The center of the nine-point circle is on the Euler line, which is just the midpoint of the connecting line between the vertical center and the outer center;
3. The nine-point circle of a triangle is tangent to the inscribed circle and three tangent circles of the triangle [Feuerbach Theorem].
4. The nine-point circle is a nine-point circle in the vertical center group, so the nine-point circle * * * is tangent to four inscribed circles and twelve circumscribed circles.
5. At nine o'clock, there are four * * * lines, the center of the circle (V), the center of gravity (G), the vertical center (H) and the outer center (O), and OG=2VG VO=2HO.
The calculation of the center of gravity coordinates of the nine-point center is as troublesome as the vertical center and the outer center.
The predefined variables are the same as those of the center of gravity and the center of gravity:
D 1, D2 and D3 are the point multiplication of the vectors whose three vertices are respectively connected with the other two vertices of a triangle.
c 1=d2d3，c2=d 1d3，C3 = d 1 D2； c=c 1+c2+c3 .
Gravity center coordinates: ((2c 1+c2+c3)/4c, (2c2+c 1+c3)/4c, (2c3+c 1+c2)/4c).