Chord length of a circle using arc lenght?

tomadom

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Nov 10, 2016
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I have a problem. I'm building a tent and can't figure something out.

I have an arc of a perfect circle which has to be of length = 10.
I also have a chord cutting a slice off this circle and from it's mid-point the height to the top of the arc is 3.
Is it possible to find the length of the chord using this information? I thought there may be a relationship between the arc length and the height of any chord a specific distance from it.

I do not know the radius of this circle.
I do not know where the center of this circle is.

I want to find the length of the red line in the picture below.
Could someone steer me in the right direction? Thanks

circle.jpg
 
I have a problem. I'm building a tent and can't figure something out.

I have an arc of a perfect circle which has to be of length = 10.
I also have a chord cutting a slice off this circle and from it's mid-point the height to the top of the arc is 3.
Is it possible to find the length of the chord using this information? I thought there may be a relationship between the arc length and the height of any chord a specific distance from it.

I do not know the radius of this circle.
I do not know where the center of this circle is.

I want to find the length of the red line in the picture below.
Could someone steer me in the right direction? Thanks

View attachment 9306

The best source I know for this is here.

You know arc length s and height (sagitta) h, which puts you in case 3. This can't be solved algebraically, but requires numerical approximation at one step. The page shows one approach to this; it could also be done by a graphing calculator, or by certain tools in a spreadsheet. The page also includes a spreadsheet that can do it for you.

Let me know if you need more help carrying this out.
 
Thanks very much for this! This is going to be very useful going forward.
 
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