I chord length and chord length formula

Chord length is the length of a line segment connecting any two points on a circle. Chord length formula, here refers to the chord length formula obtained by the intersection of straight lines and conic curves. Conic curves are some curves obtained by cutting a cone flat in mathematics and geometry (strictly speaking, a right conical surface is completely tangent to a plane), such as ellipse, hyperbola and parabola.

The formula of chord length was put forward by the ancient Greek mathematician Lefosh. Its purpose is to calculate the perimeter of a polygon and the area of a circle. This formula is also called Lefflesch chord length formula. The chord length formula is first applied to polygons, which are composed of a series of infinitesimal line segments and chords. Each chord has a length, and the circumference of a polygon is the sum of these chords.

The formula is "C=a+b+c+d+…", where c is the perimeter of the polygon, a, b, c, d, etc. Is the length of each string. In addition, the chord length formula can also be used to calculate the area of a circle. The area of a circle can be calculated by multiplying the circumference of a semicircle by the radius of the semicircle, where the circumference is a special case of the chord length formula.

The formula is expressed as "S = π r 2", where S is the area of a circle, π is pi and R is the radius of a circle. The main content of chord length formula is to calculate the length of two intersecting chords in a circle. The specific formula is as follows:

Let the center of the circle be O, the chords AB and CD intersect at E, and make straight lines perpendicular to AB and CD through O, and the intersections are F and G respectively. Then there is: the length of the string AB = | EF |×| AB |⊙| EG |. Where |EF| is the vertical height of chord AB, |AB| is the length of chord AB, and |EG| is the vertical height of chord CD.

Second, the details and precautions

1. When using the chord length formula, you need to draw a vertical line segment outside the center of the circle and mark the necessary length.

2. The principle of chord length formula is to convert the chord length problem into the calculation of triangle side length according to the similarity of triangles. So pay attention to the relationship and proportion between various lengths.

3. When two chords are parallel, the chord length formula cannot be used. At this time, other methods are needed to calculate the chord length, such as arc length formula or direct calculation.

4. In practical problems, it is sometimes necessary to approximate the chord length. At this time, the arc length formula under the arc system can be used for calculation.