## The Theorem of the Broken Chord

## by:

## BJ Jackson

This paper will explore the Theorem of the Broken Chord. The
Theorem of the Broken Chord states the following.

Given: BC > AB and E the midpoint of arc ABC.

Prove: AB + BD = DC

The paper will be broken into three parts. First, I will attempt
to convince the reader that the theorem is true using Geometer's
Sketch Pad. This will in no means be a proof, but hopefully it
will help to show that the theorem is correct and convince the
reader that it should be able to be proven.

Click **here**
to be convinced and to hopefully see how examples and technology
can help to clarify the problem for students.

Second, I will prove the Theorem of the Broken Chord.

Click **here**
for the proof of the theorem.

Finally, we will look at some extensions of the theorem. Specifically,
how the theorem leads to some of the trigonometric identities.

Click **here**
for the extensions.

If you are unable to reconstuct the picture on your own.

Click **here** for a GSP
sketch and script.

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