1. A circle is a set of points whose distance from a fixed point is equal to a fixed length. 2. The inside of a circle can be regarded as a collection of points whose distance from the center of the circle is less than the radius. 3. The outside of a circle can be regarded as a collection of points whose distance from the center of the circle is greater than the radius. 4. The same circle or the same circle has the same radius. 5. The distance from the fixed point is equal to the trajectory of the fixed-length point, and the fixed-length point is centered on the fixed point. A circle with a fixed length and a radius of 6. The locus of the point with equal distance from the two endpoints of the known line segment is the median vertical line of the line segment 7. The locus of a point with equal distance between two sides of a known angle is the bisector of this angle θ. The locus of points with equal distance from two parallel lines is a straight line with equal distance. 9. Theorem Three points that are not on the same straight line determine a circle. 10. The vertical diameter theorem bisects the chord perpendicular to the diameter of the chord and bisects the two arcs opposite to the chord 1 1. Inference 1 ① bisects the diameter (not the diameter) of the chord perpendicular to the chord, bisects the median line of two arcs whose center is opposite to the chord, bisects the diameter of an arc opposite to the chord, and bisects the chord vertically. And bisect the other arc opposite to the chord 12. Inference 2 The arcs sandwiched by two parallel chords of a circle are equal 1 12 A circle is a central symmetrical figure with the center of the circle as the symmetrical center 13. Theorem In the same circle or circle, the arcs with equal central angles are equal, and the opposite chords are equal. The distance from chord to chord of the opposite chord is equal to 14. It is inferred that in the same circle or equal circle, if one set of quantities in two central angles, two arcs, two chords or the distance between two chords are equal, the corresponding other set of quantities is equal to 15. Theorem The circular angle of an arc is equal to half the central angle, which is opposite to 16. Inference 65438+. In the same circle or in the same circle, the arc opposite to the equal circumferential angle is also equal to 17. Infer that the circumferential angle opposite to the semicircle (or diameter) is a right angle; The chord subtended by the 90 circumferential angle is 18. Inference 3 If the median line of one side of a triangle is equal to half of this side, then this triangle is a right triangle 19. Theorem The diagonals of the inscribed quadrilateral of a circle are complementary, and any external angle is equal to its internal angle of 20. ① the intersection of line l and ⊙o is D R2 1. The judgment theorem of tangent passes through the outer end of the radius, and the straight line perpendicular to the radius is the tangent of the circle 22. The property theorem of tangent line The tangent line of a circle is perpendicular to the tangent point. About 1 A straight line passing through the center and perpendicular to the tangent line must pass through the tangent point 124 Inference 2 A straight line passing through the tangent point and perpendicular to the tangent line must pass through the center 125 tangent length theorem, two tangents of the circle are drawn from a point outside the circle, and their tangent lengths are equal. The line between the center of the circle and this point bisects the included angle of the two tangents. The sum of two opposite sides of the circumscribed quadrangle of a circle is equal. The tangent angle theorem is equal to the circumferential angle of the arc pair it clamps. It is deduced that if the arcs sandwiched by two chord tangent angles are equal, then the two chord tangent angles are equal to the two intersecting chords in the chord theorem circle. The product of the length of two lines divided by the intersection is equal to 130. It can be inferred that if the chord intersects the diameter vertically, then half of the chord is the tangent and secant of the circle drawn by the middle term 13 1 from a point outside the circle according to the ratio of two line segments formed by its diameter. The tangent length is the ratio of the lengths of two lines from this point to the intersection of the secant and the circle. 132 This item infers that two secant lines are drawn from a point outside the circle, and the product of the lengths of the two lines from this point to the intersection of each secant line and the circle is equal to 133. If two circles are tangent, then the tangent point must be on the line 134① two circles are tangent to D > R+R ② two circles are tangent to d=r+r ③ two circles intersect R-R < D+R (R > R) ④ two circles are inscribed with D = R-R (R > R) ⑤ two circles contain D < R. The chord 136 theorem divides a circle into n (n ≥ 3): (1) The polygon obtained by connecting points in turn is an inscribed regular N polygon of the circle; (1) The circle passes through the tangents of each point, and the polygon whose vertices are the intersections of adjacent tangents is an circumscribed regular N polygon of the circle. These two circles are concentric circles 138. Each internal angle of a regular N-polygon is equal to the theorem (n-2) × 180/n 139, and the radius and area of the regular N-polygon are sn = pnrn/2p, where apome divides the regular N-polygon into 2n congruent right triangles 149 represents the circumference of the regular N-polygon. /4 (A stands for side length) 142 If there are k positive N corners around a vertex, the sum of these angles should be 360, so k × (n-2) 180/n = 360 is converted into (n-2) (k-2) = 4/kloc. Arc length calculation formula: L = n π r/ 180 144 Sector area formula: S sector.