Woodworking CurveDate: 02/06/2002 at 00:34:57 From: Tony Brace Subject: Radius of a circle I'm a woodworker who probably should have paid more attention when in High School so I could answer this myself. I am making a cabinet, and I want to put a curve on the front of the shelves. The "chord" of the circle would be 15" and a perpendicular line from the center point of the chord to the circumference of the circle is 1". I know there has to be an easy way to figure how long the radius of the circle is, so I can spot the point and draw the curve. Help! Date: 02/06/2002 at 03:17:52 From: Doctor Schwa Subject: Re: Radius of a circle Hi Tony, In the Dr. Math archives at: Chords of Circles http://mathforum.org/dr.math/problems/robert.02.28.01.html there is a picture to refer to: The 15" chord is the length AB in the figure. Thus AC = 7.5" Your unknown radius r is the length OA, let's say, but it's also true that OC = r - 1 (that's the 1" gap you mention). So, the right triangle OCA has r^2 = (r-1)^2 + 7.5^2 from the Pythagorean theorem, and from there it's surprisingly quick to compute the radius. Now, if you want to repay the favor, you can go visit your local high school on career day and show them what you made and how you calculated the circle so that *they* know it's time to pay attention in geometry class! Thanks for the fun question, - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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