Where c is the length of the chord, r is the radius of the circle, and ? is the angle between the two points on the circumference.įor example, if you have a circle with a radius of 10 cm and you want to find the length of the chord when ? = 30°, you would use the formula above to calculate that c = 20 cm. The formula for the chord of a circle is: The length of the chord is the distance between the two points. Formula of Chord of CircleĪ chord of a circle is a straight line that joins two points on the circumference of the circle. * Chords that are parallel to each other have equal lengths. In other words, chords that are close to being perpendicular to the radius have longer lengths. * The longer the chord, the closer it is to being perpendicular to the radius at its midpoint. * The length of the chord is always less than or equal to the diameter of the circle. The following properties hold for any chord of a circle: The length of a chord is the distance between its two endpoints. A chord can be defined by its two endpoints, or by its midpoint and one endpoint. Properties of the Chord of a CircleĪ chord of a circle is a straight line segment whose endpoints both lie on the circle. The intercepted arc creates an inscribed angle, which is equal to half the central angle. A central angle is an angle whose vertex is at the center of a circle and whose sides intercept arcs of the circle. The word chord is derived from the Latin word chorda, which means “string.” In plane geometry, a circle’s chords are line segments that intersect the circle at two points. For example, if a cord forms a 30° angle with the diameter of a circle, then you can use soh cah toa to find that:Ĭord length = diameter * sin(30°) = 10 * sin(30°) ? 8.66 units What is the Chord of a Circle?Ī circle is a simple closed curve and its chord is a line segment joining any two points on the curve. You can also use trigonometry to find the length of a cord if you know the angle that it forms with respect to the circle’s diameter. For example, if one point has coordinates (2, 3) and the other has coordinates (6, 7), then the length of the cord is: To find the length of a cord, you can use the Pythagorean theorem if you know the coordinates of the points. The length of a cord is the distance between the two points that it connects. The important thing to remember is that a cord always passes through the center of the circle. It can also be a straighter line or a curve. The word “chord” is from the Latin corda, meaning “rope,” and it’s an apt term for this geometric figure.Ī cord can be horizontal, vertical, or diagonal. Chord of CircleĪ circle’s chord is a line segment that connects any two points on the circle. In this blog post, we will explore the definition of chords and provide examples to illustrate their importance. Chords are used in a variety of mathematical applications and are a crucial part of understanding circles. The midpoint of a chord is the point on the circle that is equidistant from the endpoints of the chord. The length of a chord is the distance between the two points that it connects. A circle can have any number of chords, but some are more important than others. In geometry, a chord is a line segment that connects two points on a curve or circle. Chord of a Circle Definitions and Examples
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