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TimeStamp: 07/14/97 at 16:26:44
From: Doctor Rob
To: conni10@ibm.net (Connie)
Subject: Re: circles
Date of most recent message in thread: 07/14/97 at 17:19:14


As Connie wrote to Dr. Math
On 07/14/97 at 09:43:08 (Eastern Time),
>There is a circle with radius of 8cm. Inside a quarter of this circle
>another smaller circle is inscribed in it. What is the radius of the
>smaller circle?
>
>thanks,
>connie

Nice problem!

Drawing a diagram for this problem will help greatly.  Dr. Sarah has put a
diagram of the problem on the web at:
/dr.math/gifs/connie7.14.97.gif.  Refer to the
diagram as you read my answer.  

Draw a radius of the large circle passing through the center P of the
small circle.  Drop a perpendicular from P to one of the boundary
radii of the quarter circle, meeting it at Q.  Call the center of the
large circle O.  Then OPQ is an isosceles right triangle whose legs
are the radius r of the small circle, and so its diagonal is r*Sqrt[2].
Thus the radius of the large circle through O and P has length
r + r*Sqrt[2] = 8 cm.  Now solve for r.


-Doctor Rob,  The Math Forum
 Check out our web site!  </dr.math/>

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