How to find a chord ?

How to find a chord ?

Finding chords in a circle, in its essence - a mathematical problem, and if we talk more specifically, the task of the section geometry.That is why the use of known and proven formulas here is a must.Furthermore, the known quantities need to know the properties of a variety of constructs in a circle and its elements, and only then the desired segment joining any two points on the surface of one and the same circle, referred to as the chord is detected.

Connection between any two points on a circle with a straight - a chord.Therefore, the longest chord of a circle - its diameter.It passes this chord through the center of the circle.

Finding chords

to know how to find a chord and its length of L, decided to use the formula L = 2R ยท sin (x / 2).If you solve this problem by application, the necessary square, ruler and protractor.Using them is determined by a tension arc length, radius and circumference given the angle located between the radii of which have been carried out to the ends of the chord.

To more clearly understand how to find the length of the chord, you can use an example where the center of the circle - Oh, there's chord - AB, the angle between the radii OA and OB - x, circle radius R, and the angle as x - known.Educated ABO triangle - isosceles, because OA = OB = R. Using the formula AB = 2 * R * sin (x / 2), it turns out the length of the chord AB.

Another example, with other known parameters, will help to understand how to find the chord of the circle.Parameters: the R radius of the circle, the length of the DIA, at linking the arc, where point C is located on the circle in the middle of A and B. Using the formula, x is determined by the angle in degrees: x = (ACB * 180) / (pi * R).It only remains to substitute this expression in the previously obtained for the desired chord length: AB = 2 * R * sin ((ACB * 90) / (pi * R)).

can understand these examples that knowing two parameters required for the calculation of the length of the chord values, substituting them into the formula is determined by a third, unknown quantity.

third example - when we know the angle and length of the arc ACB.Unknown radius R.It will be equal (ACB * 180) / (pi * x).Now, this expression must be substituted into the formula for determining the length of Horta: AB = ((ACB * 360) / (pi * x)) * sin (x / 2).Now you know what a chord is and how to find it.This will help you in solving any mathematical and geometrical problems.