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A circle has a radius of 15.  Let $\overline{AB}$ be a chord of the circle, such that AB = 4.  What is the distance between the chord and the center of the circle?

 Jun 7, 2024

Best Answer 

 #1
avatar+759 
+1

Let's set the center of the circle as O. 

 

Draw a line from O perpendicular to the chord. Let this line be OM. 

\(OA = 15 \\ AM = AB / 2 = 4/2 = 2\)

 

Triangle AOM is right, with angle AMO being 90 degrees.

By using the pythagorean theorem, we have

\(OM = \sqrt{ OA^2 -AM^2} = \sqrt{ 15^2 - 2^2 } = \sqrt{221}\)

 

So sqrt221 is our answer. 

 

Thanks! :)

 Jun 7, 2024
 #1
avatar+759 
+1
Best Answer

Let's set the center of the circle as O. 

 

Draw a line from O perpendicular to the chord. Let this line be OM. 

\(OA = 15 \\ AM = AB / 2 = 4/2 = 2\)

 

Triangle AOM is right, with angle AMO being 90 degrees.

By using the pythagorean theorem, we have

\(OM = \sqrt{ OA^2 -AM^2} = \sqrt{ 15^2 - 2^2 } = \sqrt{221}\)

 

So sqrt221 is our answer. 

 

Thanks! :)

NotThatSmart Jun 7, 2024

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