Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 3"
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== Problem == | == Problem == | ||
If 3 circles of radius 1 are mutually tangent as shown, what is the area of the gap they enclose? | If 3 circles of radius 1 are mutually tangent as shown, what is the area of the gap they enclose? | ||
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| + | <center>[[Image:Usc93.3.PNG]]</center> | ||
<center><math> \mathrm{(A) \ }\sqrt{3}-\frac{\pi}2 \qquad \mathrm{(B) \ } \frac 16 \qquad \mathrm{(C) \ }\frac 13 \qquad \mathrm{(D) \ } \frac{\sqrt{3}}2 - \frac{\pi}6 \qquad \mathrm{(E) \ } \frac{\pi}6 </math></center> | <center><math> \mathrm{(A) \ }\sqrt{3}-\frac{\pi}2 \qquad \mathrm{(B) \ } \frac 16 \qquad \mathrm{(C) \ }\frac 13 \qquad \mathrm{(D) \ } \frac{\sqrt{3}}2 - \frac{\pi}6 \qquad \mathrm{(E) \ } \frac{\pi}6 </math></center> | ||
Revision as of 13:13, 23 July 2006
Problem
If 3 circles of radius 1 are mutually tangent as shown, what is the area of the gap they enclose?
Solution
Construct an equilateral triangle whose sidelengths (length 
) are composed of the radii fo the circles. The area is thus 
.
