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?
(In reply to Solution
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.