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### Chords of Circles

```
Date: 02/28/2001 at 21:59:59
From: Robert
Subject: Chords of Circles

There is a circle with radius 10 and a chord XY 8cm long. How far is
the chord from O, the center of the circle?

I cannot figure out how to do it. My book has congruent chords and the
distance to one chord, so it's in the picture and all you do is
substitute. I do not know how to start.
```

```
Date: 02/28/2001 at 22:52:13
From: Doctor Peterson
Subject: Re: Chords of Circles

Hi, Robert.

Draw the circle and chord AB. (I'll wait while you get a pencil ...)

Okay, now draw lines from the center O of the circle to the ends of
the chord, A and B.

Finally, draw a line from the center of the circle to the midpoint of
the chord, C.

Now let's look at the picture. Can you see that OC is the
perpendicular bisector of AB? That gives you a right triangle OCA. You
know the lengths of OA and AC; Pythagoras can help you find OC.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Conic Sections/Circles
Middle School Geometry

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