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

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- Oct 26th 2012, 03:59 PMjaypymneed 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

- Oct 26th 2012, 04:36 PMBobPRe: need to know the length
Look up the theorem on intersecting chords.

- Nov 1st 2012, 09:49 PMSalahuddin559Re: 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 - Nov 2nd 2012, 10:04 AMHallsofIvyRe: need to know the length
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 $\displaystyle cos(\theta)= \frac{426}{7660}= \frac{213}{3830}$. The central angle, then, is $\displaystyle 2arccos\left(\frac{213}{3830}\right)$ and the arclength is $\displaystyle 7660 \left(2arccos\left(\frac{213}{3830}\right)\right)$.