All the theorems about circles in junior high school?

Theoretically, I like the circle the most.

The eighteen theorems of the junior circle are:

1. The central angle of the circle.

Theorem: In the same circle or equal circle, the opposite arcs of the equally centered sails are equal, the opposite strings are equal, and the chord centroid distance of the opposite strings is equal.

2. Circumferential angle theorem.

The circumferential angle of an arc is equal to half of the central angle of the circle it opposes.

3. Perpendicular diameter theorem.

The diameter of a perpendicular string bisects the chord and bisects the two arcs to which the string is opposed.

4. The determination theorem of tangents: a straight dashed line that passes through the outer end of the radius and is perpendicular to the radius is the tangent of a circle.

5. Tangent length theorem: the two tangent lines that lead the circle from a point outside the circle, their tangent lengths are equal, and this point is bisected with the line at the center of the circle The angle between the two tangent lines.

6. Hail let the tangent line length theorem: if two circles have two outer tangent lines or two inner tangent lines, then the two outer tangent lines are equal in length, and the length of the two inner tangent lines is also equal. If they intersect, then the intersection must be on the concentric line of the two circles.

7. Intersecting string theorem.

Two strings intersect in a circle, and the product of the lengths of the two segments divided by the intersection is equal.

8. Cutting line theorem.

If a tangent and a secant line are drawn from a point outside the circle, the tangent length is the middle term in the ratio of the length of the two line segments from this point to the intersection point of the secant and the circle.

As follows:

1. Tangent theorem: the radius perpendicular to the tangent point; A straight line that passes through the outer end of the radius and is perpendicular to this radius is the tangent of the circle.

2. Tangent length theorem.

The two tangents from the outer point of the circle to the circle are equal in length, and the point is bisected with the line in the center of the circle.

3. The secant theorem.

The product of the two secant lines leading the circle from the point outside the circle to the distance of each secant from the intersection of the circle is equal.

4. Vertical diameter theorem.

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

5. The chord tangent angle theorem.

The chord chamfer angle is equal to the corresponding circumferential angle.

1. The area of the semicircle: s semicircle = (r 2) 2. (r is the radius).

2. The area of the ring: S big circle - S small circle = (r 2-r 2) (r is the radius of the large circle, r is the radius of the small circle).

3. The circumference of the circle: c=2 r or c=d. (d is the diameter, r is the radius).

4. The circumference of the semicircle: d+(d) 2 or d+ r. (D is the diameter, R is the radius).

5. The length of the fan arc l=the central angle.

radian) r = n r 180 ( is the central angle of the circle) (r is the radius of the fan). Repentance.

6. Bi lacks fan-shaped area.

s = n r 360 = lr 2 (l is the arc length of the fan).

7. The radius of the bottom surface of the cone r=nr 360 (r is the radius of the bottom surface) (n is the central angle).

1.Perpendicular diameter theorem: The string is squared perpendicular to the diameter of the string and bisects the arc opposite the string.

2.The diameter of the bisector chord (not the diameter) is perpendicular to the chord, and the arc to which the bisector chord is opposed.

3.The straight arc of the bisector arc is the chord of the perpendicular bisector of the arc.

4.In the same circle or equal circle, the arcs corresponding to the central angles of the same circles are equal, and the corresponding strings are also equal.

5.In the same circle or equal circle, the central angles of the same circle are equal to the chord centroid distance of the two strings.

6.In the same circle or equal circle, if one pair of two central angles, two arcs, two chords, and two chord centricities are equal, then the other pairs corresponding to them are equal.

7.Circumferential angle theorem: The degree of a circumferential angle is equal to half of the number of angles at the center of the arc to which it is opposed.

8.The circumferential angle of the semicircle (or diameter) is a right angle.

The circumferential angle of the chord is the diameter.

10.In the same circle or equal circle, the circumferential angles of the same or equal arcs are equal; The arcs opposite the circumferential angles that are equal are also equal.

11.The theorem of the circumscribed quadrilateral within the circle: the diagonal complementarity of the circumscribed quadrilateral within the circle.

12.There is the following theorem in the positional relationship between a straight 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.

dr, then the line l is separated from o.

13.The theorem that a straight line is tangent to a circle: a straight line with a radius that passes through the outer end of the radius type and is perpendicular to this radius is a tangent of a circle.

14.Tangent theorem of a circle: The radius passing through the tangent is perpendicular to the tangent of the circle.

15.Tangent length theorem: The two tangents of a circle made by a point outside the circle are of equal length.

16.Triangle inscribed circle:

A triangle is at an equal distance from one vertex to two tangents on its two adjacent edges.

17.The distance from the right-angled vertex of a right-angled triangle to the tangent point on the right-angled edge is equal to the radius of the inscribed circle.

18.Half of the product of the circumference of the triangle and the radius of its inscribed circle is equal to the area of the triangle.

The distance from each point on the circle to the center of the circle is equal;

The three vertices of the triangle determine a circle, which is the circumscribed circle of the triangle, and the center of the circumscribed circle is the intersection of the perpendicular bisector of the three sides of the triangle;

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

The diameter of the bisector chord (not the diameter) is perpendicular to the chord, and the two arcs of the bisector chord are opposed.

In the same circle or equal circle, the arcs opposite the central angles of the circle are equal, and the chords are equal.

In the same circle or equal circle, if one set of quantities is equal in two central angles, two arcs, and two strings, then the rest of the quantities corresponding to them are equal.

The circumferential angle of an arc is equal to half of the central angle of the circle to which it is opposite, and in the same circle or equal circle, the circumferential angle of the same arc or equal arc is equal; The circumferential angle of the diameter is a right angle, and the chord of the circumferential angle of 90° is the diameter;

The circle is complemented diagonally by the quadrilaterals.

The tangent of the circle is perpendicular to the diameter passing through the tangent point.

From the outer point of the circle, two tangents of the circle can be drawn, and their tangents are of equal length, which is bisected by the line at the center of the circle.

The center of the inscribed circle of the triangle is the intersection of the bisector of the corners of the triangle, which is called the heart of the triangle.

The formula for arc length: l = n r 180, r is the radius of the circle, and n° is the degree of the central angle of the circle to which the arc is opposed.

The formula for the area of the sector is: s=n r 360, r is the radius of the circle, and n° is the degree of the central angle of the circle opposite the arc.

A circle is in a plane, and the line segment oa rotates around one of its fixed endpoints o, and the shape formed by the other endpoint a is called a circle. Its fixed endpoint o is called the center of the circle, and the line segment oa is called the radius.