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C is the centre of two concentric circles. AB is a tangent to the smaller circle and a chord of the larger circle. The radius of the smaller circle is 6 cm. Chord AB = 16 cm. Calculate the radius of the larger circle.

Guest Nov 10, 2015

Best Answer 

 #2
avatar+78755 
+10

The radius of the larger circle  = 10 cm

 

Here's a pic....

 

A radius drawn to a tangent meets that tangent at right angles. Thus, the radius of the smaller circle - OC - meets the tangent chord AB at right angles. And the radius of the larger circle meets the chord AB at right angles. And, by Euclid, a radius  meeting a chord at right angles bisects that chord. So, triangle AOC is a 6 - 8 - 10 "Pythagorean Triple" right triangle with leg OC = 6 and leg AC = 8.   And the hypotenuse - OA - equals  the radius of the larger circle, i.e., 10 cm.

 

 

cool cool cool

CPhill  Nov 10, 2015
edited by CPhill  Nov 10, 2015
edited by CPhill  Nov 11, 2015
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3+0 Answers

 #1
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+10

ok

imagine that you draw a line from where the chord meets the larger circle to the centre - this is line A

the radius is line B

the chord - from point A to its midpoint is line C

ABC is a triange

BUT it is a right angled triangle

use pythagoras

side A = X

side B = 6

side C = 8

8squared + 6squared = xsquared = 100

x = 10

you will notice that this is also the radius of the larger circle!

ta dah!

hope this helped

Guest Nov 10, 2015
 #2
avatar+78755 
+10
Best Answer

The radius of the larger circle  = 10 cm

 

Here's a pic....

 

A radius drawn to a tangent meets that tangent at right angles. Thus, the radius of the smaller circle - OC - meets the tangent chord AB at right angles. And the radius of the larger circle meets the chord AB at right angles. And, by Euclid, a radius  meeting a chord at right angles bisects that chord. So, triangle AOC is a 6 - 8 - 10 "Pythagorean Triple" right triangle with leg OC = 6 and leg AC = 8.   And the hypotenuse - OA - equals  the radius of the larger circle, i.e., 10 cm.

 

 

cool cool cool

CPhill  Nov 10, 2015
edited by CPhill  Nov 10, 2015
edited by CPhill  Nov 11, 2015
 #3
avatar+91051 
0

 

That is a really good answer guest.    Thanks

 

Great pic Chris.   laugh

Melody  Nov 10, 2015

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