SOLUTION: A circle has a chord of length 8 that is tangent to a smaller, concentric circle.Find the area between the two circles: a) 16 (note each of the answers listed have a pie sign

Question 146646: A circle has a chord of length 8 that is tangent to a smaller, concentric circle.Find the area between the two circles:
a) 16 (note each of the answers listed have a pie sign next to them.)
b) 9
c) 24
d) 36
e) none

Again THANK YOU !!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
It always helps to draw a picture

note: "R" is the radius of the larger circle and "r" is radius of the smaller circle. Also, I divided the chord in half.

From the picture, we can see that the radius R is the hypotenuse of the triangle with legs of "r" and 4. So this means

Square 4 to get 16

Subtract from both sides

So

Now the area of the larger circle is and the area of the smaller circle is

Since we want the area between the two circles, we must subtract the two areas to get:

Factor out the GCF

Plug in . In other words, replace with 16

Rearrange the terms

So the area between the two circles is
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