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3 cents (Posted on 2014-08-29) Difficulty: 3 of 5
Place two pennies on a table each touching a third, but not each other. The centers of the three form a certain angle.

For what angle will the area of the convex hull of this shape be maximized?

No Solution Yet Submitted by Jer    
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re: Solution | Comment 2 of 3 |
(In reply to Solution by Bractals)

I calculated the area of the triangle as


Base = length(BC) = 4a*sin(x)
Height = 2a*cos(x)
Area = Base*Height / 2 = 4*a^2*sin(x)cos(x)

I guess it works out the same, using a half-angle formula.

Interesting, I had never payed attention to how to derive the half-angle formula, and I guess this does it.

  Posted by Steve Herman on 2014-08-30 10:11:58
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