# Thread: need to know the length

1. ## need to know the length

If I have a circle with the circumference of 7660mm and a straight line bisecting it 426 mm down from the center then what is the length of the arc between the points on the circle and how do I find this

2. ## Re: need to know the length

Look up the theorem on intersecting chords.

3. ## Re: need to know the length

From the circumference, find the radius. From this, and the fact that the line bisects 426mm below center, find the angle that the line segment makes at center. Get it?

Salahuddin
Maths online

4. ## Re: need to know the length

Originally Posted by jaypym
If I have a circle with the circumference of 7660mm and a straight line bisecting it 426 mm down from the center then what is the length of the arc between the points on the circle and how do I find this
I assume that "426 mm down" means that the line from the center of the circle is perpendicular to the chord. Those lines together with the radii from the center of the circle to the ends of the chord give you two right triangles. Each has hypotenuse 7660 and "near side" of length 426 so that $cos(\theta)= \frac{426}{7660}= \frac{213}{3830}$. The central angle, then, is $2arccos\left(\frac{213}{3830}\right)$ and the arclength is $7660 \left(2arccos\left(\frac{213}{3830}\right)\right)$.