Final answer:
To determine the chord length between two points on a circle, use the formula for the sector's arc length and the central angle. Multiply the angle (in radians) by the circle's radius to find the arc length, which is approximately equal to the chord length.
Step-by-step explanation:
To find the length of a chord between two points on the circumference of a circle, you can use the formula for the arc length of a sector and the central angle that subtends the arc. The length of the chord can be directly related to the arc length if we consider it as a 'slice' or sector of a circle. The formula for the circumference of a circle is 2πr, where π is approximately 3.14159 and r is the radius of the circle. If the circle is rotated through an angle Δθ, the arc length (Δs) is equal to the rotation angle (Δθ) times the radius (r).
Therefore, if you know the central angle Δθ in radians and the radius of the circle, you can calculate the arc length and subsequently the chord length using the following formula: arc length (Δs) = Δθ × r. When the central angle is given in degrees, first convert it into radians (multiply by π/180) before applying the formula. This method was known by ancient Greeks and relates to uniform circular motion, where every point moves through the same angle in a given time.
If the chord is a straight line, then the approximation c ≈ c' holds true, and the length of the chord is equivalent to the arc length described.