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### Finding the Table's Diameter

```
Date: 05/05/2001 at 22:36:46
From: Sarah
Subject: What is the diameter...

A circular breakfast table is pushed into the corner of a room so that
it touches both walls. On the edge of the table is a scratch 8 inches
from one wall and 9 inches from the other wall. What is the diameter
of the table?

I have tried to draw many pictures, the way my teacher told me to, but
```

```
Date: 05/06/2001 at 17:36:39
From: Doctor Jaffee
Subject: Re: What is the diameter...

Hi Sarah,

Try this. On a piece of graph paper let the origin be the corner of
the room, the positive x-axis be one wall and the positive y-axis be
the other wall. If you pick any point at random to be the center of
the circle, you can see that you are restricted to picking a point
whose distance from the one wall equals the distance to the other
wall. In other words, you have to pick the center to be a point on the
line y = x.

Assume that the scratch is at the point (8,9). Or, you could put it at
the point (9,8). It makes no difference.

Now, you should be able to see that the distance from the center to
the point (8,9) must be the same as the distance from the center to
either of the two walls. Can you make that into an equation with one
variable? If you can, you should be able to solve the problem.

Give it a try and if you want to check your answer with me, write
back. If you are having difficulties, let me know and show me what you
have done so far, and I'll try to help you some more.

Good luck.

- Doctor Jaffee, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Conic Sections/Circles
High School Equations, Graphs, Translations
High School Geometry
Middle School Conic Sections/Circles
Middle School Geometry
Middle School Graphing Equations

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