Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 3"
| Line 1: | Line 1: | ||
== 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? | ||
| + | {{image}} | ||
<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> | ||
| Line 9: | Line 10: | ||
== See also == | == See also == | ||
* [[University of South Carolina High School Math Contest/1993 Exam]] | * [[University of South Carolina High School Math Contest/1993 Exam]] | ||
| + | |||
| + | [[Category:Introductory Geometry Problems]] | ||
Revision as of 10:05, 23 July 2006
Problem
If 3 circles of radius 1 are mutually tangent as shown, what is the area of the gap they enclose?
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
Solution
Construct an equilateral triangle whose sidelengths (length 
) are composed of the radii fo the circles. The area is thus 
.
