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There are two circles of equal radius 1 that are centered at points A and B, respectively, and externally tangent to each other. A tangent DC is drawn to both circles, and a square EFGH fits between the circles such that points G and H lie on the line segment DC.

Find the side length of the square.

 

 Dec 30, 2020
 #1
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Can you show where you started?

 Dec 30, 2020
 #2
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It would be very helpful if you could present your strategy, my strategy was to use to variables, x as the length of the square and y as the length of GC and DH since they are equal

Guest Dec 30, 2020
 #3
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There are two circles of equal radius 1 that are centered at points A and B, respectively, and externally tangent to each other. A tangent DC is drawn to both circles, and a square EFGH fits between the circles such that points G and H lie on the line segment DC.

Find the side length of the square.

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∠DNM = ∠EDM = tan-1(1/2)

 

DE = sin∠DNM * DN 

 

EH = sin∠EDM * DE

 

The side length of the square, GH = 2/5 units  smiley

 

 Dec 31, 2020

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