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### Stewart's Theorem

```
Date: 5/18/96 at 18:7:7
From: Anonymous
Subject: Information on Stewart's Theorem

Hi,

I have to give a lesson/report on Stewart's Theorem, and am
looking for information on history, uses (in "real life" or in
math), examples, or anything else that might be useful. I know
the theorem, its proof, and a minimal history of the proof.
I've searched and so far have come up with very little.
Thank you for any information you might be able to provide.

Michael Sonsino
```

```
Date: 5/23/96 at 13:56:8
From: Doctor Betsy
Subject: Re: Information on Stewart's theorem

Hi Michael,

I found some information on Stewart's Theorem in the archives of the
World Wide Web, the address for the information is at

http://mathforum.org/kb/message.jspa?messageID=1074570

Here is a little of what I found.

On Wed, 22 Mar 1995, REBECCA BROWN wrote:

I'm looking for any information on Stewart's Theorem.  Any help on
this topic will be greatly appreciated.

Rebecca,

You might want to check out Posamentier's "Excursions in Advanced
Euclidean Geometry" (an excellent resource for any geometry class!)
It has a short section on Stewart's Theorem along with several
applications of it to triangles.

Stewart's Theorem: Let d be the length of a Cevian of a triangle that
divides the opposite side of length c into segments of length m and n
adjacent to the sides of length a and b respectively. Then
na^2+mb^2 = c(d^2+mn). (See crudely drawn picture below.)

/\
/  \\
/    \ \
/      \  \
a /      d \   \ b
/          \    \
/     m      \  n  \
----------------------
c

Sandy Norman
University of Texas at San Antonio

Hope that helps.

-Doctor Betsy,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons

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