find the lenth of chord
Answers
Step-by-step explanation:
r is the radius of the circle. c is the angle subtended at the center by the chord.
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Chord Length Formula.
Formula to Calculate Length of a Chord
Chord Length Using Perpendicular Distance from the Center Chord Length = 2 × √(r2 − d2)
Chord Length Using Trigonometry Chord Length = 2 × r × sin(c/2)
Answer:
Chord of a Circle Definition
The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle. The figure below depicts a circle and its chord.
Chord Of Circle
In the given circle with ‘O’ as the center, AB represents the diameter of the circle (longest chord), ‘OE’ denotes the radius of the circle and CD represents a chord of the circle.
Let us consider the chord CD of the circle and two points P and Q anywhere on the circumference of the circle except the chord as shown in the figure below. If the endpoints of the chord CD are joined to the point P, then the angle ∠CPD is known as the angle subtended by the chord CD at point P. The angle ∠CQD is the angle subtended by chord CD at Q. The angle ∠COD is the angle subtended by chord CD at the center O.
Angle Subtended by Chord
Chord Length Formula
There are two basic formulas to find the length of the chord of a circle which are:
Formula to Calculate Length of a Chord
Chord Length Using Perpendicular Distance from the Center Chord Length = 2 × √(r2 − d2)
Chord Length Using Trigonometry Chord Length = 2 × r × sin(c/2)