Sunday, March 8, 2015

3/8/15

An equilateral triangle of side length 2 is drawn on a plane.  4 circles are drawn on the plane as well.  The first is the circumcircle of the triangle, and the rest have the same radius as the first, and are centered at each of the vertices of the triangle.  Find the area of the region only occupied by exactly two of the 4 circles.

Hint: Draw the diagram.  Which circles can fit into the description?

Hint 2: Now that you know what the region is, there are a few parts of the diagram whose area is hard to calculate.  Is there any way to cancel them out?

Level: 5

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