# Combining Computer Science and Math: Inscribing a Circle in a Triangle Using the Geometry Applet

## Abstract

Here is a project that combines Computer Science and Mathematics. Prove a method for inscribing a circle within a triangle (as shown). You'll also learn how to create an interactive diagram to illustrate your proof, using an applet that runs in your Web browser. If you like solving problems and thinking logically, you'll like this project.## Objective

This project has two objectives:- write a mathematical proof for the construction of a circle inscribed in a triangle;
- illustrate the proof with a dynamic figure created with the Geometry Applet.

## Credits

## Cite This Page

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### APA Style

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I Did This Project! Please log in and let us know how things went.Last edit date: 2014-06-20

## Introduction

The illustration below shows a circle, with center at point*D*, inscribed within triangle

*ABC*. By definition, an inscribed circle is tangent to the three sides of the triangle.

This project has two objectives:

- write a mathematical proof for the construction of a circle inscribed in a triangle;
- illustrate the proof with a dynamic figure created with the Geometry Applet.

What is the Geometry Applet? It is a very cool program written by Professor David Joyce to illustrate an online version of Euclid's *Elements*. The applet creates dynamic diagrams in which you can manipulate the geometric figures by clicking and dragging on points. You program the applet much like creating a geometrical construction by hand, so as the points are dragged, all of the essential relationships in the diagram remain intact. It is an engaging and intuitive way to illustrate the generality of your proof. To see an example of the Geometry Applet in action, see any of these three projects:

Throwing You Some Curves: Is Red or Blue Longer?

Thinking in (Semi-)Circles: The Area of the Arbelos

Chain Reaction: Inversion and the Pappus Chain Theorem

To learn how to use the Geometry Applet to create your own dynamic diagrams, see:

Getting Started with the Geometry Applet

## Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:- the concept of a tangent point,
- congruent triangles,
- bisection of an angle.

## Bibliography

- The Math Forum at Drexel University has some good advice on how to build a mathematical proof:

http://mathforum.org/library/drmath/view/54693.html - There are many more examples in their FAQ section:

http://mathforum.org/dr.math/faq/faq.proof.html - For help with the programming the Geometry Applet, see:

Getting Started with the Geometry Applet - The Geometry Applet was kindly provided to Science Buddies by its author, Professor David Joyce, who wrote it for illustrating an amazing online edition of Euclid's
*Elements*:

http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

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*Note:*A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed

## Materials and Equipment

- For completing the proof manually, all you'll need is:
- pencil,
- paper,
- compass, and
- straightedge.

- For creating a dynamic diagram of the proof using the Geometry Applet, you will also need:
- a computer,
- a text editor (Notepad will work fine),
- a Web browser program (e.g., Internet Explorer or Firefox).

- For a live demonstration along as part of your display, a laptop computer is recommended.

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Experimental Procedure

- Do your background research,
- organize your known facts, and
- spend some time thinking about the problem and you should be able to come up with the proof.

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Variations

- Corollary: prove that the lines bisecting the three vertex angles of a triangle share a common intersection point.

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Ask an Expert

The Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.Ask an Expert

## Related Links

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*Note:*A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed

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