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 
I just can't get it. Please help! Thanks.

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/