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Geek Culture / Circle math question. Chord to diameter?

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Lost in Thought
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Posted: 20th Aug 2005 06:25 Edited at: 20th Aug 2005 06:25
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If you have a circle of unknown size but you know the length of a chord (21.350") and the height (distance from the center of the chord to the outside of the circle) of 6.480" ... can you get the diameter from this info? If so what is the formula? Any help is appreciated.

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Jess T
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Posted: 20th Aug 2005 07:50
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If you think about it, it's not impossible...

There can only be one circle ( given that the height is less than the radius ) with a chord of that length which is that height from the edge.

How you would work it out, though... I don't know.

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hyrichter
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Posted: 20th Aug 2005 08:20
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It's actually very easy. I was spending forever with tangents, cosines, etc., when it hit me...similar triangles! I wish I could draw a picture here for you, but what you do is set up an equation like this:

6.48/10.675 = 10.675/x

10.675 is half of the chord length, and x is the dimension from the chord to the bottom of your circle. So, you solve for x using cross products and get 17.5857. Then you add in the 6.48 and you get 24.0657 as the diameter of your circle.

I hope I told you correctly...it's kinda late here.


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Lost in Thought
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Posted: 20th Aug 2005 11:35
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Sounds good to me. I gave up and wrapped a string around it and got 24.114 so thats pretty close (can't complain about .043 of an inch)

Thank you.

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spooky
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Posted: 20th Aug 2005 14:25
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There are a few different ways to calculate it. Two are on this page;

http://en.wikipedia.org/wiki/Circle

Radius = ((L/2)^2 + D^2) / 2D

where L is length of chord and D is distance from hlafway along chord to circle edge

you get 24.065742

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