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Three unit circles are drawn so they are mutually tangent, as shown below. A blue circle that is externally tangent to all three unit circles is drawn. Finally, three red circles are drawn, so that each red circle is externally tangent to two unit circles and externally tangent to the blue circle. Then the radius of each red circle can be expressed in the form

 

\(\frac{a - b \sqrt{c}}{d}\)

where a, b, c, and d are positive integers, when simplified. Find the sum of a, b, c,and d.

 Dec 22, 2021
 #1
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The radius of the red circle is $\frac{9 - 2 \sqrt{3}}{5}$, so the answer is 9 + 2 + 3 + 5 = 19.

 Dec 22, 2021
 #2
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it was wrong

Guest Dec 22, 2021
 #3
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oops...here's the pic of the prob:

 

 

Guest Dec 22, 2021
 #4
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Blue circle radius = 0.154700538

 

Red circle radius = 0.06278172

 

That's all that I have so far. laugh

 Dec 22, 2021

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