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# Lengths in Circles

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74
5
+184

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
+1

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

Apr 10, 2021
#2
+1

Guest Apr 10, 2021
#3
+144
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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
+184
+1

It's right! Thank you

Apr 10, 2021
#5
+118626
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Very nice, James   !!!!

Apr 10, 2021