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

Algebra ->  Quadratic-relations-and-conic-sections -> 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      Log On


   

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) About Me  (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.



circle


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

4%5E2%2Br%5E2=R%5E2


16%2Br%5E2=R%5E2 Square 4 to get 16


16=R%5E2-r%5E2 Subtract r%5E2 from both sides


So R%5E2-r%5E2=16

Now the area of the larger circle is A=pi%2AR%5E2 and the area of the smaller circle is A=pi%2Ar%5E2


Since we want the area between the two circles, we must subtract the two areas to get: pi%2AR%5E2-pi%2Ar%5E2


pi%28R%5E2-r%5E2%29 Factor out the GCF pi


pi%2816%29 Plug in R%5E2-r%5E2=16. In other words, replace R%5E2-r%5E2 with 16


16pi Rearrange the terms


So the area between the two circles is 16pi