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### Woodworking Curve

```
Date: 02/06/2002 at 00:34:57
From: Tony Brace

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

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/
```
Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Practical Geometry

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