Woodworking Curve

Date: 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/