University of South Carolina High School Math Contest/1993 Exam/Problem 3

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.

$\mathrm{(A) \ }\sqrt{3}-\frac{\pi}2 \qquad \mathrm{(B) \ } \frac 16 \qquad \mathrm{(C) \ }\frac 13 \qquad \mathrm{(D) \ } \frac{\sqrt{3}}2 - \frac{\pi}6 \qquad \mathrm{(E) \ } \frac{\pi}6$

Solution

Construct an equilateral triangle whose sidelengths (length $2$ ) are composed of the radii fo the circles. The area is thus $\sqrt{3}-\pi/2$ .

Page

Toolbox

Search

University of South Carolina High School Math Contest/1993 Exam/Problem 3

Problem

Solution

See also