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Mathematics-Online problems:

Interactive Problem 184: Tangent Circles

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The figure shows an equilateral triangle with side length 1. Each vertex of the triangle is also the center of a circle with radius $ r > 0$. These three circles are tangent to another circle with radius $ s$.

\includegraphics[width=0.5\linewidth]{Kreise}
  1. How many different possibilities exist for the touching circle with radius $ s$ if $ r=1/2$ and $ r\neq 1/2$?
  2. Determine the values of the possible radii $ s$ for the case $ r=1/4$.


Solution:

  1. if $ r=1/2$:     possibilities
    if $ r\neq 1/2$:     possibilities
  2. $ s_1=$
    $ s_2=$
    $ s_3=$
    $ s_4=$
    (The values of the radii $ s$ should be stated in ascending order and correct to two decimal places.)

   
(From: Day of Mathematics 1998)
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  automatically generated: 2/ 6/2018