How to calculate Chord Length of a Circle

How to calculate chord length

Let a circle with a known radius R be given, its chord L bends an arc φ, where φ is defined in degrees or radians. In this case, calculatethe lengthchordsaccording to the following formula: L = 2 * R * sin (φ / 2), substituting all known values.
Consider a circle with a center at the point O and a given radius. The sought are two identicalchordsAB and AC with one point of intersection with the circle (A). It is known that the angle formed by the chords is based on the diameter of the figure. Perform a graphical construction of the specified elements in a circle. Lower the radius from the center O to the intersection point of the chords A. The chords will form a triangle ABC. To determine the lengths of the same chords, use the properties of the resulting isosceles triangle (AB = AC). The VO and OS segments are equal (AU by condition - diameter) and are the radii of the figure, therefore, the AO is the median of the triangle ABC.
How to calculate <b> length </ b> <strong> chords </ strong>
According to the property of an isosceles triangle, its median is also the height, that is, perpendicular to the base. Consider the resulting AOB right triangle.The leg of the OB is known and is equal to half the diameter, that is, R. The second leg of the joint-stock company is also defined as the radius R. From here, using the Pythagorean theorem, express the unknown side AB, which is the desired chord of the circle. Calculate the final result AB = √ (AO² + OV²). By the condition of the problem, the length of the secondchordsAC is equal to AB.
Suppose a circle is given with a diameter D and a chord CE. At the same time, the angle formed by the chord and diameter is known. Calculatethe lengthchordsYou can, using the following construction. Draw a circle centered at point O and a CE chord, draw a diameter through the center and one of the pointschords(FROM). It is known that any chord connects two points of a circle. Drop from the second point of its intersection with the circle (E) in the center O the radius of the EO. Thus, we obtain an isosceles CEO triangle with the base chord CE.

Video: How to Measure Chords in Circles : Algebra, Geometry & More

How To Calculate Length Of Chord For Circle
How to calculate chord length

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