Concentric Circles

Apr 2010
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0
Two concentric circles have radii 3 and 7 cm. Find, to the nearest hundredth, the length of a chord of the larger circle that is tangent to the smaller circler.

I tried drawing it out, but could not make the connections. Any help would be greatly appreciated. Also please show steps that way I know how you did them any why you did them.
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Two concentric circles have radii 3 and 7 cm. Find, to the nearest hundredth, the length of a chord of the larger circle that is tangent to the smaller circler.

I tried drawing it out, but could not make the connections. Any help would be greatly appreciated. Also please show steps that way I know how you did them any why you did them.
Is this the answer?
\(\displaystyle 4\sqrt{10}=12.65\)
 
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pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
This is how i'm reading it.

The chord will go from one side of the bigger circle just touching the smaller circle. Plot 2 relations \(\displaystyle x^2+y^2= 3^2\) and \(\displaystyle x^2+y^2= 7^2\) and draw the line, using the relations you should be able to find the length.

\(\displaystyle 2\times \sqrt{49-3^2}\)
 
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Jun 2009
806
275
Two concentric circles have radii 3 and 7 cm. Find, to the nearest hundredth, the length of a chord of the larger circle that is tangent to the smaller circle.

.
Let O be the center of the concentric circles. Let AB be the chord which touches the smaller ciecle at D.

Now AO is the radius of the larger circle.

OD is the radius of the smaller circle.

ADO is a right angled triangle.

So \(\displaystyle AD^2 = OA^2 - OD^2\)

And AB = 2AD.

Now solve.
 
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