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Two circles of radius 10 cm overlap such that each circle passes through the center of the other, as shown. How long, in cm, is the common chord (dotted segment) of the two circles? Express your answer in the simplest radical form.

 Apr 10, 2021
 #1
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+1

Chord length = 2[sqrt(102 - 52) = 10√3

 Apr 10, 2021
 #2
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cheeky

Guest Apr 10, 2021
 #3
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Here is the picture

\(\angle A=\angle B=\angle C=60^\circ \)

tringangle ABC is an equilateral triangle because AC, AB, BC are all radius, so the length is same

The length of the common chord :

\(2\times \sqrt{10^2-5^2}=2\times 5\sqrt{3}=10\sqrt{3}\)

 Apr 10, 2021
 #4
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It's right! Thank you

 Apr 10, 2021
 #5
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Very nice, James   !!!!

 

 

cool cool cool

 Apr 10, 2021

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