perplexus.info :: Geometry : Circular intersection

Circular intersection (Posted on 2003-05-06)

If you remember how Venn Diagrams looked with the three intersecting circles, that is the context for this puzzle.

There are three circles, circle A, circle B, and circle C. Each circle passes through the center of the other two. What is the area of the intersection of these three circles?

Submitted by Gamer

Rating: 2.6667 (3 votes)

Solution: (Hide)

Since all three cirles have a common radius, you the distance between two circle centers is the same as the radius. So, if you connect the centers of these circles, it creates an equilateral triangle.
Noting that if you add two of these smaller triangles to the wanted area, it makes 1/2 of a circle, you get (pi*r^2)/2-(s(3)*r^2)/2 or ((pi-s(3)/2)*r^2, where s() means square root of. In other words, the answer is half of (pi minus the square root of three) times the radius squared.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	Antonio	2003-09-03 07:41:33
Agreement	Brian Nowell	2003-05-09 21:26:53
solution	Fahim	2003-05-06 06:54:05
solution	Charlie	2003-05-06 03:12:53

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