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 Circular Fun (Posted on 2005-07-28)
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.

 Subject Author Date Requested solution Justin 2006-01-20 09:09:02 The solution akash 2005-12-31 12:09:42 re(2): A triangle Tristan 2005-11-23 17:55:05 re: A triangle Mindy Rodriguez 2005-11-22 23:57:51 different ronwilliams 2005-11-09 10:30:22 i agree ronwilliams 2005-11-09 10:23:42 i think jamie 2005-10-19 22:34:37 No Subject devendra kumar 2005-08-22 02:01:43 re(2): solution..... :) Bret 2005-08-02 20:37:34 re: solution..... :) josh_79_97 2005-08-01 22:20:37 solution..... :) josh_79_97 2005-08-01 21:50:45 "externally tangent"=? Jason Taylor 2005-07-30 03:07:20 i agree punchmancan 2005-07-29 08:41:22 solution? Reges 2005-07-28 17:09:36 re: A triangle nikhil 2005-07-28 08:19:07 re(2): A Bermuda triangle brianjn 2005-07-28 07:16:58 re: A Bermuda triangle Ady TZIDON 2005-07-28 06:48:48 A triangle brianjn 2005-07-28 06:15:37

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