Theorem 1 16 The circumferential angle of an arc is equal to half the central angle of an arc. Infer that the circumferential angles of the same arc or equal arc are equal. In the same circle or equal circle, the arc opposite to the equal circle angle is also equal. 1 18 infers that 2 semicircles (or diameters) are right angles; The chord subtended by the circumferential angle of 90 is 1 19 Inference 3 If the median line of one side of a triangle is equal to half of this side, then this triangle is the diagonal complement of the inscribed quadrilateral of the right triangle 120 theorem circle. And any outer angle is equal to the intersection point of the inner diagonal line 12 1① and ⊙o D R 122 passes through the outer end of the radius, and the straight line perpendicular to this radius is the tangent of the circle. 124 Inference 1 A straight line passing through the center and perpendicular to the tangent must pass through the tangent point 125 Inference 2 A straight line passing through the tangent point and perpendicular to the tangent must pass through the center 126 The tangent length theorem leads to two tangents 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 13 1. It is deduced that if the chord intersects the diameter vertically, then half of the chord is the tangent and secant of the circle, which is drawn by the middle term 132 according to the ratio of two line segments formed by a point outside the circle. The tangent length is the ratio of the lengths of two lines from this point to the intersection of the secant and the circle. 133 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 134. If two circles are tangent, then the tangent point must be on the line 135① 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 137 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 139. Every inner angle of a regular N-polygon is equal to the radius and area of the regular N-polygon in theorem (n-2) × 180/N 140, where apome divides the regular N-polygon into 2n congruent right-angled triangles 14 1. The area √ 3a/4a indicates that the side length is 143. If there are K positive N corners around a vertex, since the sum of these angles should be 360, k× (n-2) 180/n = 360 is converted into (n-2)(k-2)=4 144. The calculation formula of arc length is L = nπ r/ 180 145. The formula of sector area is s sector. 147 The two feet of an isosceles triangle are equal. 148 The bisector of the top angle, the median line on the bottom edge and the height on the bottom edge of the isosceles triangle coincide. 149 If the two angles of a triangle are equal, then the opposite sides of the two angles are also equal. 150 A triangle with three equal sides is called equilateral triangle mathematical induction. It is generally proved that a triangle is equal to a positive integer. (2) Assuming that n = k (the first value of k ≥ n, and k is a natural number), it is proved that the proposition is also true when n=k+ 1. Factorial: n! = 1× 2× 3× …× n, (n is an integer not less than 0) specifies 0! = 1。 Permutation, combination, permutation take all permutation numbers of m elements in n different elements, A(n, m)= n! /m！ (m is a superscript, n is a subscript, and both are integers not less than 0, m ≤ n). Taking m elements from n different elements at a time, no matter what order they are combined into a group, is called combination. Species number of all different combinations C(n, m)= A(n, m)/(n-m)! =n！ /〔m！ (n-m)！ ) (m is a superscript, n is a subscript, and both are integers not less than 0, m≤n) ◆ The properties of the combination number: c (n, k) = c (n, k- 1)+c (n- 1, k-1); For the combination number C(n, k), n and k are converted into binary respectively. If n corresponding to a binary bit is 0 and k is 1, then c (n, k) is an even number; Otherwise, it is the odd binomial theorem (a+b) n = c (n, 0) × a n× b 0+c (n, 1) × a (n- 1 )× b+c (n, 2) 2)+...+c (n, There is a definition in the centripetal neighborhood of. If there is a constant A, there is always a positive number δ for any given positive number ε (no matter how small it is), so that when X satisfies inequality 0.