Question

How do I find an arc length using chords?

Answer 1

A chord on a circle will make up one side of an isosceles triangle, with the other two sides having length equal to the radius
`r` of the circle. So if you know the length of the chord, you can find the central angle subtended by the chord (the angle between the sides with length
`r`).

If the chord has length
`x`, then the central angle
`\theta` can be found with some basic trig:


`\sin\frac\theta2=\frac{\frac x2}r=\frac x{2r}`

Once you find
`\theta`, you can find the arc length
`L` using the relation


`\frac L\theta=(2\pi r)/(2\pi)\implies L=r\theta`