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Circular Fun (Posted on 2005-07-28) Difficulty: 2 of 5
When you draw three circles of radius r such that all three are externally tangent, what is the area of the shape in the center in terms of r?

  Submitted by Justin    
Rating: 3.2857 (7 votes)
Solution: (Hide)
sqrt(3)r^2-pi(r^2)/2

This solution is achieved by drawing simple math.

Take the distance between the centers of two circles (2r) and make it into the sides of an equilateral triangle.

You now find the height of the triangle: sqrt((2r)^2-(r^2)) = sqrt(3)r.

Now find the area of the triangle by subbing in sqrt(3)r as h. b=2r, so A=2sqrt(3)r^2/2 so A=sqrt(3)r^2.

Subtract the three sixths of the circles(each angle is 60 degrees), to get sqrt(3)r^2-pi(r^2)/2.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionRequested solutionJustin2006-01-20 09:09:02
The solutionakash2005-12-31 12:09:42
re(2): A triangleTristan2005-11-23 17:55:05
Questionre: A triangleMindy Rodriguez2005-11-22 23:57:51
differentronwilliams2005-11-09 10:30:22
i agreeronwilliams2005-11-09 10:23:42
i thinkjamie2005-10-19 22:34:37
No Subjectdevendra kumar2005-08-22 02:01:43
Some Thoughtsre(2): solution..... :)Bret2005-08-02 20:37:34
Solutionre: solution..... :)josh_79_972005-08-01 22:20:37
solution..... :)josh_79_972005-08-01 21:50:45
"externally tangent"=?Jason Taylor2005-07-30 03:07:20
i agreepunchmancan2005-07-29 08:41:22
solution?Reges2005-07-28 17:09:36
Some Thoughtsre: A trianglenikhil2005-07-28 08:19:07
re(2): A Bermuda trianglebrianjn2005-07-28 07:16:58
Solutionre: A Bermuda triangleAdy TZIDON2005-07-28 06:48:48
SolutionA trianglebrianjn2005-07-28 06:15:37
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