Circle Radius from Chord Length and DepthDate: 06/16/99 at 02:18:52 From: Jacques Duranleau Subject: Finding Radius of circle knowing only chord and depth. How do you find the radius or diameter of a circle when you only know a chord length and the depth? In this case, the chord does not pass through the center. Date: 06/16/99 at 08:45:46 From: Doctor Peterson Subject: Re: Finding Radius of circle knowing only chord and depth. Hi, Jacques. You can almost find this formula in our FAQ on circles. On this page, scroll down to Segment of a Circle: http://mathforum.org/dr.math/faq/formulas/faq.circle.html Unfortunately, it's not quite there, though you could work it out from what is there, namely c = ... = 2 sqrt[h(2r-h)] You have h (the height of the chord) and c (the length of the chord), and need to find r, so you can solve this for r as r = (c^2/(4h) + h)/2 c^2 + 4 h^2 = ----------- 8h You can work out the formula this way: *********** ***** ***** **** /| **** ** / | ** * / | * ** r / | ** * / |c/2 * * / | * * / | * * / r-h | h * * *--------+------------* * \ | * * \ | * * \ | * * \ | * ** \ | ** * \ | * ** \ | ** **** \| **** ***** ***** *********** We have a right triangle, and Pythagoras gives: r^2 = (r-h)^2 + (c/2)^2 r^2 = r^2 - 2rh + h^2 + c^2/4 2rh = h^2 + c^2/4 h^2 + c^2/4 4h^2 + c^2 r = ----------- = ---------- 2h 8h I hope that meets your needs. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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