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

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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?
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Answer by ikleyn(52835)   (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    and  its area is   = ;

     the radius of the smallest     circle is    and  its area is   = .


     The area of the greatest circle is   = .


The shaded area is   -  -  = .


The fraction of the shaded area is   = .    ANSWER

Solved.



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