1986 AJHSME Problems/Problem 23
Revision as of 22:18, 23 January 2009 by 5849206328x (talk | contribs) (New page: ==Problem== The large circle has diameter <math>\text{AC}</math>. The two small circles have their centers on <math>\text{AC}</math> and just touch at <math>\text{O}</math>, the center o...)
Problem
The large circle has diameter 
. The two small circles have their centers on and just touch at 
, the center of the large circle. If each small circle has radius 
, what is the value of the ratio of the area of the shaded region to the area of one of the small circles?
![[asy] pair A=(-2,0), O=origin, C=(2,0); path X=Arc(O,2,0,180), Y=Arc((-1,0),1,180,0), Z=Arc((1,0),1,180,0), M=X..Y..Z..cycle; filldraw(M, black, black); draw(reflect(A,C)*M); draw(A--C, dashed); label("A",A,W); label("C",C,E); label("O",O,SE); dot((-1,0)); dot(O); dot((1,0)); label("$1$",(-.5,0),N); label("$1$",(1.5,0),N); [/asy]](http://latex.artofproblemsolving.com/7/4/f/74f7ba33bdc6fad777668c3830583aad49e61377.png)
Solution
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