SOLUTION: In the diagram, AB is the diameter of the large circle. The smaller circles both have their centres on AB, and both are tangent to each A other and to the large circle. If AC is th

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: In the diagram, AB is the diameter of the large circle. The smaller circles both have their centres on AB, and both are tangent to each A other and to the large circle. If AC is th      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1208874: In the diagram, AB is the diameter of the large circle. The smaller circles both have their centres on AB, and both are tangent to each A other and to the large circle. If AC is the length of AB, what fraction of the diagram is shaded?
https://ibb.co/DtCYH1c
Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.

For simplicity (and without loss of generality), we may think that AB = 2,  
so the radius of the greatest circle is 1.


Then the radius of the intermediate circle is  5%2F7  and  its area is  pi%2A%285%2F7%29%5E2 = pi%2A%2825%2F49%29;

     the radius of the smallest     circle is  2%2F7  and  its area is  pi%2A%282%2F7%29%5E2 = pi%2A%284%2F49%29.


     The area of the greatest circle is  pi%2A1%5E2 = pi.


The shaded area is  pi - pi%2A%2825%2F49%29 - pi%2A%284%2F49%29 = pi%2A%2820%2F49%29.


The fraction of the shaded area is  %28pi%2A%2820%2F49%29%29%2Fpi = 20%2F49.    ANSWER

Solved.