There are times in life when the knowledge acquired during schooling, are very useful.Although at the time studying this information seemed boring and unnecessary.For example, how to use the information on how the chord length is?We can assume that for specialties not related to the exact sciences, such knowledge is of little use.However, we can cite many examples (from a New Year's costume design to complex devices airplane) when problem-solving skills in geometry are superfluous.
term "chord»
This word means "string" is translated from the language of the homeland of Homer.It was introduced by mathematicians of the ancient period.Jordi designate the section of elementary geometry of the straight line that combines any two points of a curve (circle, parabola or ellipse).In other words, the binder is a geometric element on the line intersecting a given curve at several points.In the case of a circle chord length lies between two points of the figure.
part of the plane bounded by a line intersecting the circle, and it is called the arc segment.It may be noted that toward the center of the chord length increases.Part circle located between the two points of intersection of the straight line is called the arc.It is a measure of the central angle.The vertex of the geometric figure is a circle in the middle, and whose sides bear against the intersection point of the chord with the circle.
Properties and formulas
length of the chord of the circle can be calculated by the following conditional expression:
L = D × Sinβ or L = D × Sin (1 / 2α), where β - the angle at the vertex of the triangle inscribed;
D - diameter of the circle;
α - central angle.
There are some properties of this segment, as well as other figures associated with it.These points are shown in the following list:
- Any chord located at the same distance from the center, have the same length, while the converse is also true.
- All angles are inscribed in a circle and rest on a common segment that joins two points (with their tops are in the same side of the element) are identical in magnitude.
- biggest chord is a diameter.
- sum of any two corners if they are based on the active segment, but their vertices lie at different sides with respect to it, is 180 °.
- Big chord - compared with similar, but less element - lies closer to the middle of the geometric figure.
- all corners that are entered and are based on the diameter of 90˚.
other calculations to find the length of the arc, which lies between the endpoints, you can use the formula of Huygens.This requires such action:
- p denote the unknown quantity, and the chord bounding this part of the circle will be named AB.
- We find the midpoint of AB and perpendicular to it will deliver.It may be noted that the diameter of a circle drawn through the center of the chord, it forms a right angle.Converse is also true.At this point, where the diameter passing through the center of the chord is in contact with the circle is denoted by M. Then
- segments AM and BM, respectively, may be called as l and L.
- arc length can be calculated using the following formula: r≈2l +1/3 (2l-L).It may be noted that the relative error of this expression increases with increasing angle.Thus, when 60˚ it is 0.5% and for an arc equal 45˚, this value is reduced to 0.02%.
Chord length can be used in various fields.For example, the calculation and design of flanged connections, which are common in the art.One can also see in the calculation of this value to determine the ballistics of the bullet flight distance and so on.
