高中数学公式(理科必备)（The high school mathematics formula(Essential Science)）The mathematical formula of mathematical formula, is the number of different things in nature between representation or other or unequal relationship, it exactly reflects the relationship between the internal and external things, we arrived at another thing from a thing for make us better understand the connotation and essence of things.As some basic formulaY = ax * BX parabola: + CY is equal to the square of ax plus BX plus CWhen a > 0 opening upA < 0 when opening downWhen C = 0 after the origin of parabolaB = 0 parabolic symmetry axis is the Y axisThere are vertex type y = (x+h) * a + kY is equal to a times the square of +k (x+h)-h is the vertex coordinates of the XK is the vertex coordinates of the YGenerally used to find the maximum value and minimum valueThe standard parabolic equation: y^2=2pxIt is said that the focus of the parabola in X positive half axis, the focus of coordinates (p/2,0) alignment equation is x=-p/2As the focus of the parabola in any half shaft, so there are standard y^2=2px y^2=-2px x^2=2py x^2=-2py equationRound: Volume =4/3 (PI) (r^3)Area = (PI) (r^2)The perimeter of the =2 (PI) rThe standard equation of circular (x-a) 2+ (y-b) 2=r2 (Note: A, b) is the center coordinatesX2+y2+Dx+Ey+F=0 note: D2+E2-4F>0 general equation of the circle(a) calculation formula of ellipse circumferenceOval circumference formula: L=2 - b+4 (a-b)Oval circumference theorem: equal to the perimeter of an ellipse ellipse short axle length radius circumference (2 - b) and the four times of the elliptical semimajor axis (a) and theshort axle length difference (B).(two) the calculation formula of ellipse areaEllipse area formula: S= PI abEllipse area theorem: ellipse area equal to PI (PI) by the elliptical semimajor axis (a) and the short axle length (b) of the product.The elliptical perimeter and area formula although no elliptic ZhouLv T, but the two formulas are through elliptic ZhouLv T derived evolution. Constant for the body, for the use of formula.Long radius * short radius *PAI* calculation formula of ellipse ellipse object high volumeTrigonometric function:The horns and formulaSin (A+B) =sinAcosB+cosAsinB sin (A-B) =sinAcosB-sinBcosACos (A+B) =cosAcosB-sinAsinB cos (A-B) =cosAcosB+sinAsinBTan (A+B) = (tanA+tanB) / (1-tanAtanB) Tan (A-B) = (tanA-tanB) / (1+tanAtanB)Cot (A+B) = (cotAcotB-1) / (cotB+cotA) cot (A-B) = (cotAcotB+1) / (cotB-cotA)Double angle formulaTan2A=2tanA/ (1-tan2A) cot2A= (cot2A-1) /2cotaCos2a=cos2a-sin2a=2cos2a-1=1-2sin2aSin +sin (alpha +2 alpha PI /n (+sin) +2 *2/n +sin (alpha PI) alpha PI + +2 *3/n)...... +sin[+2 alpha pi * (n-1) /n]=0Cos +cos (alpha +2 alpha PI /n (+cos) +2 *2/n +cos (alpha PI) alpha PI + +2 *3/n)...... +cos[+2 alpha pi * (n-1) and /n]=0Sin^2 (alpha) +sin^2 (alpha PI -2 /3 +sin^2 (+2) alpha PI /3) =3/2TanAtanBtan (A+B) +tanA+tanB-tan (A+B) =0Four double angle formula:Sin4a = 4 * (* Sina (SINA * * 2 ^ 2 - 1)Cos4a = 1 + (- 8 * 8 * Thing Thing ^ ^ 2 + 4)Tan4a = (4 * 4 * Tana Tana - ^ 3) / (1 - 6 * Tana Tana ^ ^ 2 + 4)五倍角公式:Sin5a = 16sina ^ 5 ^ 3 + - 20sina 5sinaCos5a = 16cosa ^ 5 ^ 3 + - 20cosa 5cosaTan5a = * (5 to 10 * Tana Tana Tana ^ ^ 2 + 4) / (1 - 10 ^ 2 + 5 * * Tana Tana ^ 4)六倍角公式:Sin6a = 2 * (SINA (SINA * * 2 * * (2 + 1) * Sina - 1) * (- 3 + 4 * Sina ^ 2))Cos6a = ((- 1 + 2 * thing ^ 2) * (16 * 16 * Thing Thing 4 ^ - ^ 2 + 1))Tan6a = (6 + 20 * * Tana Tana Tana ^ ^ 3 - 6 * 5 / (- 1) ^ 2 + 15 * 15 * Tana Tana Tana ^ ^ 4 + 6)七倍角公式:Sin7a = ((56 * * - Sina Sina Sina 112 * ^ ^ 2 - 4 - 6 * 7 + 64 Sina ^))Cos7a = ((56 * thing * ^ 2 ^ + - 112 * 64 * Thing Thing 4 ^ 6 - 7))Tan7a Tana * = (7 ^ 2 + 35 * 21 * Tana Tana Tana ^ 6 ^ 4 + / (- 1) ^ 2 + 21 - 35 * * Tana Tana Tana * ^ 4 + 7 ^ 6)八倍角公式:Sin8a = (- 8 * * * thing Sina (SINA - 2 * 2 ^ (- 1) * 8 * 8 * 2 + Sina Sina ^ ^ 4 + 1))Cos8a = 1 + (160 * 256 * Thing Thing 4 ^ - ^ 6 + 128 * thing * ^ 8 - 32 thing ^ 2)Tan8a = - (- 1 * 8 * Tana Tana ^ 2 + 7 * 7 * Tana Tana ^ 6 ^ 4 + / (- 1) ^ 2 + 28 * 70 * Tana Tana ^ 4 - 28 * Tana Tana ^ ^ 6 + 8)九倍角公式:Sin9a = (SINA * (- 3 + 4 ^ 2 * Sina (SINA) * 64 * ^ 6 ^ 4 + 96 * 36 * Sina Sina ^ 2 - 3)Cos9a (* = (- 3 + 4 * thing ^ 2) * (64 * thing ^ 6 ^ 4 + 96 * 36 * Thing Thing ^ 2 - 3)Tan9a = (9 - 84 * * Tana Tana ^ 2 + 126 * 36 * ^ 4 - Tana Tana Tana ^ ^ 6 + 8) / (1 - 36 ^ 2 + 126 * * Tana Tana Tana - 84 * ^ 4 ^ 6 + 9 * Tana ^ 8)十倍角公式:Sin10a = 2 * (* * Sina (4 ^ 2 + 2 * * Sina (SINA) - 1 * 4 * 2 * 2 - Sina Sina ^ (- 1) * 20 * ^ 2 + 5 + Sina Sina 16 * ^ 4)Cos10a = (- 1) ^ 2 + 2 * Thing (Thing) * 256 * ^ 8 - 512 * thing ^ 6 + 304 * 48 * Thing Thing 4 ^ - ^ 2 + 1))Tan10a = - 2 * * (5 - 60 * Tana Tana Tana 126 ^ ^ 2 + 4 * 60 * Tana Tana ^ ^ 6 + 5 * 8) / (1 + a ^ 2 - 210 45 * * 210 * Tana Tana ^ 4 + 6 ^ - ^ 8 + 45 * Tana Tana ^ 10)·万能公式:2Tan sinα = (alpha / 2) / [1 + a ^ 2 (alpha / 2)]Cosα = (1 - a ^ 2 (alpha / 2)] / [1 + a ^ 2 (alpha / 2)]2Tan tanα = (alpha / 2) / (1 - a ^ 2 (alpha / 2)]半角公式Without (/ 2) = - (- 1) / 2) = (A / 2) (- sqrt (- 1) / 2) Cos (A / 2) = sqrt ((+ 1) / 2) cos (A / 2) = sqrt ((+ 1) / 2) So (A / 2) = - (- 1) / ((1 +)) (A / 2) = - (1 - (-) / ((1 +))COT (A / 2) = sqrt ((1 +) / ((1 -) COT (A / 2) = sqrt ((1 +) / (- 1))和差化积Without 2sinacosb = (A + b) + (A - b) without 2cosasinb = (A + b) - (A - b)2cosacosb = cos (A + b) - (A - b) - 2sinasinb = cos (A + b) - cos (A - b)Sina sinb + = 2sin ((A + b) / 2) cos ((A + b) / 2 = 2cos thing cosb ((A + b) / 2) sin ((A - b) / 2)Tana Tunb = no + (A + b) / cosacosb Tana Tunb = (A - b) / cosacosbCotbsin Elevation + (A + b) / sinasinb cotbsin cota + (A + b) / sinasinb某些数列前n项和1 +2 +3 +4 +5 +6 +7 +8 +9 +... + N = N (n + 1) / 2 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 +... + (2n - 1) = N22 + 4 + 6 + 8 + 6 + 12 + 14 +... + (2n) = N (n + 1) ^ 2 + 2 ^ 2 +3 ^ 2 +4 ^ 2 +5 ^ 2 +6 ^ 2 +7 ^ 2 +8 ^ 2 +... + n ^ 2 = n (n + 1) (2n + 1) / 61 ^ 3 +2 ^3 + 3 ^ 3 +4 ^ 3 +5 ^ 3 +6 ^ 3 ^ 3 +... = (N (n + 1) / 2) ^ 2 (1 + 2 + 3 * 2 * 3 * 4 * 5 + 4 + 5 + 6 * 6 *7 + + N (n + 1) = N (n + 1) (n + 2) / 3.正弦定理 Sina sinb = A / B / C / 注 = = sync: 其中表示三角形的外接圆半径 R 2R余弦定理 A2 = B2 + C2 2accosb 注: 角b是边a和边c的夹角乘法与因式分 A2 - B2 = (A + b) (a-b) A3 + B3 = (A + b) (A2 + B2 B3 A3 - AB) = (A - B (A2 + B2 + AB)三角不等式 | | < a + B + B | to | | | | - | < B + B to | | | | | to | ≤b < = > - b≤a≤b| a-b | > | to | - | B | - | to | ≤a≤ | to |一元二次方程的解 - B + sqrt (B2 - 4ac) / 2a - B - sqrt (B2 - 4ac 2a) /根与系数的关系 x1 + x2 = - B / x1 * x2 = C / a 注: 韦达定理判别式 B2 - 4th 注方程有相等的两实根 = 0:B2 - 4ac > 0 注: 方程有两个不相等的个实根B2 - 4ac < 0 注: 方程有共轭复数根公式分类公式表达式圆的标准方程 (X -) 2 + (- b) 2 = R2 注: (A, b) 是圆心坐标圆的一般方程 x2 + y2 + DX + Ey + F = 0 注: D2 + E2 4F > 0抛物线标准方程 2px y2 = x2 y2 = x2 2PY 2px - = = - 2PY直棱柱侧面积 S = C * h * H = c 's 斜棱柱侧面积正棱锥侧面积 S = 1 / 2C * H '正棱台侧面积 S = 1 / 2 (C + C' h ')圆台侧面积 S = 1 / 2 (C + c) (R + L = pi r l s = 4pi) 球的表面积 * R2圆柱侧面积 S = C * h * H = 2Pi 圆锥侧面积 S = 1 / 2 * C * * * L = pi r l弧长公式 L = a * R > 0 a是圆心角的弧度数r 扇形面积公式 S = 1/ 2 * L * R锥体体积公式 v = 1 / 3 * s * H 圆锥体体积公式 v = 1 / 2 * pi * R2H斜棱柱体积 v = S' l 's 注: 其中, 是直截面面积, l是侧棱长柱体体积公式 v = S * h * v = PI 圆柱体 R2H图形周长面积体积公式长方形的周长 = (+ 宽×2 长)正方形的周长 = 边长×4长方形的面积 = 长×宽正方形的面积 = 边长×边长三角形的面积已知三角形底a, 高h, 则s＝ah / 2已知三角形三边a, B, C, 半周长p, 则s＝ - [P (P -); (b) (P - c)] (海伦公式) (P = (A + B + c) / 2)和: (A + B + c) * (A + B - c) * 1 / 4已知三角形两边a, B, 这两边夹角c, 则s＝absinc / 2设三角形三边分别为a、b、c, 内切圆半径为rIs the triangle area = (a+b+c) r/2Set the three sides of a triangle are respectively a, B, C, a radius of R=abc/4r is the area of a triangleThe known three sides of a triangle a, B, C, S = {1/4[c^2a^2- (V (c^2+a^2-b^2) /2 (^2]}) "three oblique quadrature" Qin Jiushao in the Southern Song Dynasty)| a B 1 |S =1/2 C D 1 | * || E F 1 || [a B 1 || C D 1 | three order determinant, the triangle ABC in plane Cartesian coordinate system A (a, b), B (C, d), C (E, f), where ABC| E F 1 |Take the best selection in counterclockwise order starting from the right corner, because it made the results are generally positive, if not according to the rules, may be negative, but it does not matter, as long as you can get the absolute value, the size of the triangle area will not be affected! ]Qin Jiushao triangle middle area formula:V [S= (Ma+Mb+Mc) * (Mb+Mc-Ma) * (Mc+Ma-Mb) * (Ma+Mb-Mc)]/3 The Ma, Mb, Mc for the median of a triangle.The area of a parallelogram bottom = xArea = trapezoidal (bottom + bottom) * / 2Radius diameter = x 2 / 2 = radius diameterThe perimeter of a circle diameter = x = PiPi * * 2 radiusThe area of a circle radius radius = pi * *Surface area = cuboid(length x width x + + long high width * height) * 2Volume = length * width * heightThe surface area of the cube edge = length x length x 6 Volume of cuboids = length * * long edge edge lengthThe flank area = underside of the circumference of a circle * highThe cylindrical surface area = bottom surface area + wall area V = x high cylindrical bottom areaThe volume of the cone bottom area = x height / 3Cuboid (cube and cylinder)The volume of the bottom area of x = highThe plane figureThe perimeter and area of S C designationSquare a side length C = 4AS = A2The rectangular A and B side length C = 2 (a+b)S = abTriangle a, B, C three sideOn the edge of the high HaHalf of the circumference of SA, B, C.S = /2 S = ah/2 (a+b+c)SinC = ab/2?= [s (S-A) (S-B) (S-C)]1/2= a2sinBsinC/ (2sinA)1 points and only a straight line2 the shortest line between two points3 the same angle or isometric equal margin4 with the angle of the complement of equal or constant5 a little bit and only a straight line and the vertical line is knownThe 6 line a point and the straight line connecting all the points on the line, vertical line is the shortest7 parallel lines through a point outside the axiom, and onlya straight line with the parallel line8 if the two line and third line parallel to the two lines are parallel to each other9 corresponding angles are equal, the two parallel lines10 alternate angles are equal, the two parallel lines11 complementary interior angles on the same side, two parallel lines12 the two parallel lines, corresponding angles are equal13 two line parallel, alternate angles are equal14 the two parallel lines, complementary interior angles on the same side15 theorems on both sides of the triangle is greater than the third sideThe 16 sides of the triangle that is less than third edges17 triangle triangle sum theorem three angles and equal to 180 degrees18 corollary two acute 1 right triangles are complementary19 a corollary of a triangle is equal to the 2 corners and two angles it is adjacent and20 a corollary of a triangle with 3 corners than any one and it is not adjacent.The corresponding 21 congruent triangle edge, corresponding angle.The 22 corner edge axiom (SAS) there are two congruent triangleson both sides and their corresponding equal angle23 corner corner axiom (ASA) has two triangles congruent horns and their edges corresponding to the equal24 inference (AAS) had two horns and one of the angle on the side corresponding to the equal two congruent trianglesThe 25 side edge axiom (SSS) has two triangles congruent three sides corresponding to the equal26 hypotenuse, right angle side axiom (HL) is the hypotenuse and a right angle side corresponding to the equal two congruent right triangles27 theorem 1 in the bisector of angle point to a distance equal to the angle on both sidesBoth sides of the 28 theorem 2 to a corner of the distance from the same point in the bisector of angleBisector of angle 29 is the set of all points to both sides of the angle of equal distanceTwo and 30 are equal isosceles triangle theorem of an isosceles triangle (i.e. equal equilateral angle)31 corollary 1 isosceles triangle vertex bisection bisector and perpendicular to the bottom hemThe high overlap between bottom 32 isosceles triangle anglebisector, the median and the bottom edge of the33 corollary 3 equilateral triangles whose angles are equal, and each angle equal to 60 degreesTheorem 34 isosceles triangle if a triangle has two angles are equal, then the two corners of the edge are equal (of equiangular equilateral)35 corollary 1 three angles are equal triangle is an equilateral triangle36 corollary 2 isosceles triangles with one angle equal to 60 degrees is an equilateral triangle37 in a right triangle, if a sharp angle equal to 30 degrees so it on the right angle side is equal to the hypoteneuse half38 the hypotenuse is equal to the hypoteneuse half lineThe 39 line is equal to the distance theorem on the perpendicular bisector of the line and two points40 inverse equal theorem and a line two points distance point in this line perpendicular bisector41 the perpendicular bisector of the line segment can be regarded as equal to the set of all points and segment ends distance42 theorem 1 on a linear symmetric two figure is congruent43 theorem 2 if two graphics on a linear symmetry, then the symmetry axis is corresponding line perpendicular bisector theorem 44 3 two graphics on a linear symmetric, if they intersect the corresponding segment or extension line, then the intersection at the axis of symmetry45 If the corresponding inverse theorem of two graphics attachment is a straight line perpendicular bisector, then the two graphics on the line of symmetry46 Pythagorean theorem of right triangle two right angle sides a, b square, and the square is equal to the hypotenuse C,a^2+b^2=c^247 the Pythagorean theorem and inverse theorem of a, if the three side of triangle B, C a^2+b^2=c^2,The triangle is a right triangleIn theorem 48 quadrilateral and equal to 360 degrees49 quadrilateral corners and is equal to 360 degreesIn the 50 polygon sum theorem n edge shape and is equal to (n-2) * 180 degrees51 any inference multilateral angle and equal to 360 degrees52 parallelogram theorem 1 parallelogram shaped equal diagonal53 parallelogram theorem 2 of the opposite sides of the parallelogram is equal54 corollaries caught in the parallel line between the two parallel lines of equal55 parallelogram Theorem 3 parallelogram diagonals bisect each other56 parallelogram determined quadrilateral theorem 1 two diagonal parallelogram is equal respectively.57 parallelogram theorem 2 equal two groups respectively on the edge of the quadrilateral is a parallelogram58 quadrilateral parallelogram Theorem 3 diagonal parallelogram is split each other59 parallelogram theorem 4 a set of edges parallel equal quadrilateral is a parallelogramFour angles of 60 rectangular theorem 1 rectangle is right61 rectangular rectangle 2 equal diagonal theorem62 theorem 1 rectangle has three corners is a quadrilateral rectangular rectangle63 theorems of rectangular parallelogram 2 diagonal equal rectangle64 diamond theorem 1 Diamond four edges are equalThe diagonal 65 diamond theorem 2 diamond perpendicular to each other, and each diagonal split a set of diagonalHalf of the 66 diamond area = diagonal product, namely s= (a * b) / 2To determine the 67 diamond quadrilateral theorem 1 quadrilateral are equal is diamondParallelogram 68 diamond theorem 2 diagonal perpendicular to each other is a diamondThe 69 square theorem four angles of 1 square is a right angle. The four sides are equalThe 70 square theorem 2 square two diagonals are equal and mutually perpendicular bisector, each diagonal bisecting a set of diagonal71 theorem 1 the center symmetric two figure is congruent.72 theorem 2 the center symmetric two graphics, symmetric point connection by symmetric center, and is a center of symmetry split73 If the corresponding inverse theorem of two graphics connection after a certain point, and this point is split, then the two figure on this point symmetryTwo angles in the same at the end of the 74 isosceles trapezoid isosceles trapezoid theoremThe two diagonals equal 75 isosceles trapezoid76 trapezoid isosceles trapezoid theorem in the same on the bottom of the two corners is equal isosceles trapezoidThe 77 diagonal is equal trapezoid isosceles trapezoid78 parallel lines line bisection theorem: if a set of parallel lines in a straight line section of the line is equal, so in other segments of straight line intercepts are equal79 corollary 1 after a trapezoidal waist straight midpoint and bottom parallel, will divide a waistThe 80 side of the triangle midpoint after corollary 2 with the other side will split the third parallel straight edge81 triangles in the bit line bit line theorem triangle parallel to the third side, and equal to half of itThe 82 trapezoidal median line bit line parallel to the trapezoidal theorem at the end of two, and l= two and the bottom half (a+b) / 2 s=l * h83 (1) if the proportion of basic properties of a:b=c:d, so ad=bc if ad=bc, then a:b=c:d84 (2) than the nature if the A / b=c / D, then (a + b) / b=(c + D) / D85 (3) geometric properties if the A / b=c / d=... =m / N (b+d+... +n (a+c+ = 0), then... (b+d+ / +m)... +n =a / b)86 parallel lines dividing the segments is proportional to theorem three parallel lines cut two lines, the corresponding segment income proportionThe 87 side of the straight line parallel to the inference triangle section on both sides (or other extension lines on both sides), the corresponding segment income proportion88 if a straight line section theorem of two sides of the triangle (extension line or on both sides of the corresponding segments) in proportion, so this line is parallel to the third sides of the triangle89 parallel to the side of the triangle, and the intersection line and other sides, which is truncated by the three side of the triangle and the three sides of a triangle is proportional to the correspondingThe 90 line parallel to the side of the triangle theorem and the other two sides (extension line or on both sides of the intersection, a triangle) and similar to the original triangle91 similar triangles theorem 1 corners equal two triangles (ASA)The 92 is the hypotenuse of a right triangle high into two righttriangles and triangles.93 theorem 2 on both sides of the corresponding proportion and angle equal to two triangles (SAS)94 theorems 3 three sides corresponding proportion, two triangles (SSS)Theorem 95 If the hypotenuse of a right angled triangle and a right angle side and another hypotenuse and a right angle side corresponding proportion, then the two right angled triangle similarity96 theorem 1 similar triangles corresponding to high ratio, corresponding to the midline than with the corresponding angle bisector ratio is equal to the similarity ratio97 theorem 2 similarity ratio equal to the perimeter of the triangle similarity ratio98 Theorem 3 of similar triangle area ratio is equal to the square of the ratio of similarity99 sine random acute value equal to its angle cosine value, the cosine value of arbitrary angleIt is the complement of the value in the sineTangent 100 any acute angle value equal to its complement of the cotangent value, any sharp cotangent value equal to the value of the tangent angleThe 101 round is a fixed distance equal to the length of the point set102 inside the circle can be regarded as a collection of center distance is less than the radius of the pointThe 103 round can be regarded as the center of the external set distance is greater than the radius of the pointWith 104 or so is equal to the radius of the circle105 to a given distance point trajectory is designated as the center of the fixed length of the circle radiusThe 106 line is equal to the distance and known two endpoints of the locus of points, is a line perpendicular bisector107 to the known angle on both sides of the distance equal point trajectory is the angular bisector108 to two equal distance parallel lines the locus of points is a straight line, and the two parallel lines are parallel and equidistant.109 theorems in three points on the same line of a circle.110 vertical theorem perpendicular to chord diameter bisecting the string and the bisection chord of two arcs111 corollary 1 (not the bisection chord diameter perpendicularto chord diameter),And divide the arc chord twoThe perpendicular bisector of a chord passes through the centre and divide the arc chord twoThe bisection chord a the arc diameter perpendicular bisector of chord, and another bisection chord of the arc112 corollary 2 round two parallel strings clamped by the equal arcThe 113 circle is the center of symmetry to the center center of symmetry114 theorems in the same circle or congruent circles, arc equal central angle of, the chords are equal, equal to the string string from the heartIn the 115 round and round in the inference or, if there is a group that is equal to the amount of their corresponding amount of other groups are equal to two central angle, two arcs, two strings or two strings of the string in the distanceIs a 116 circle theorem of the arc angle it to the central angle of the half117 corollary 1 with arc or arc on the circle with equal angles; or circle, equal circumferential angle of the arc are equal118 corollary 2 semicircle (or diameter) on the circumference of the right angle is 90 DEG; the circumference of the chord diameterCorollary 3 if 119 triangles on one side of the line is equal to the side of the half, then the triangle is a right triangleComplementary diagonal inscribed quadrilateral 120 circle theorem, and any one corner is equal to its inner diagonal121 lines L and O intersect, d < RThe L and O / d=r tangent lineThe linear L and O from D / > RThe 122 theorem of tangent radius after the outer end of the straight and perpendicular to the radius of the circle is tangentTheorem 123 tangent tangent circle perpendicular to the radius through the tangent point124 corollary 1 passes through the centre and straight line perpendicular to the tangent point will pass125 corollary 2 through the tangent point and line perpendicular to the tangent of the center will pass126 tangent two tangent length theorem from the outer circle point lead round, two tangent lengths are equal, the anglebetween the center and the point of the line bisection two tangent127 round circumscribed quadrilateral two group of boundary and equalThe 128 angle is equal to the circumference of the clamping angle theorem of arc angle129 that if the two angle between the arc are equal, then the two angle is equal130 the intersection of two intersecting chord chord theorem within the circle, the two lines are divided into the intersection of long equal area131 corollary if string and diameter vertical intersection, then it is about half the diameter of the string into theTwo line mean proportional132 cutting line theorem from the outer circle point lead circle tangent and secant, tangent length is to cut itThe two lines long line and circle intersection mean proportional133 corollary two a bit from the round a secant lead round, the two point line to each line and the circle of intersection of the length of the same product134 If the two circle, then the point must be in the line of every135 of the two outer circle from d > r+r in the two round cut d=r+rThe two circle intersection R-R < d < r+r (R, R)The two circle is inscribed d=r-r (R, R) the two round with D (r > R) < R-RThe 136 theorem of the intersection of two round connecting line perpendicular bisector of two round of public stringDivide the circle into 137 theorems of n (n = 3):The connecting points of the polygon in turn is the circle inscribed regular n polygon.After all the points are tangent to a circle, the intersection adjacent vertex tangent polygon is the circle tangent regular n polygon.138 any theorem polygon has a circumscribed circle and a circle, these two circles are concentricEach corner 139 regular n polygon is equal to (n-2) * 180 degrees / nThe 140 theorem is n edge shape and the radius of the right triangle is apothem n edge into 2n etc.N is 141 sided area of sn=pnrn / 2 P positive n perimeter edge shapeThe 142 is the triangle area root 3A / 4 a side said143 If there are k positive n edge shape angle around a vertex, because these angle and stress360 degrees, so k * (n-2) / n=360 degrees to 180 degrees (n-2) (K-2) =4The 144 arc length formula: l=n R / 180 piThe 145 sector area formula: s sector =n PI R2 / 360=lr / 2146 common tangent length = d- (R-R) Grandpa tangent length = d- (r+r)Two foot 147 equal isosceles triangleHigh overlap bottom 148 isosceles triangle angle bisector, on line, on the bottom149 if a triangle with two equal angles, then the two corners of the edge are equal150 triangle with three equal sides is called equilateral triangleBaidu's Wikipedia entry for reference only, if you need to solvespecific problems(especially in law, medicine and other fields), you are advised to consult professionals in related fields. This entry to help meOne thousand two hundred and ninety-eightThis document from the Internet, can only be used for learning exchanges! (a person is ChaoContribution: everyone has a dream!)。
