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The circle centered at \((2,-1)\) and with radius \(4\) intersects the circle centered at \((2,5)\) and with radius \(\sqrt{10}\) at two points \(A\) and \(B\). Find \((AB)^2.\)

 Jul 2, 2020
 #1
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The coordinates of the intsersection are ((24 + sqrt(455))/12, 31/12) and ((24 - sqrt(455))/12, 31/12).  Then AB = sqrt(455)/6, so the answer is 455/36.

 Jul 2, 2020
 #2
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That is not the answer.

 Jul 2, 2020
 #3
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(AB)2 = 3.8729833462 = 15 

 

I have drawn these two circles and realized that the distance from the center of a larger circle to AB is 3.5, and the distance from the smaller circle's center to AB is 2.5. After that, it was easy to calculate the length of AB.

 Jul 2, 2020
 #4
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(AB)2 = 3.872983346= 15 

 

I have drawn these two circles and realized that the distance from the center of a larger circle to AB is 3.5, and the distance from the smaller circle's center to AB is 2.5. After that, it was easy to calculate the length of AB.  smiley

 Jul 2, 2020

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