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/
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