#
*Finding a loose cover of a triangle with circles
whose total area is minimal*

Consider an arrangement of circles covering the
total area of an equilateral triangle. Assume that the length of the sides
of the triangle is 1 and that each of the three circles centred at the
corners of the triangle all have the same radius. Which arrangement has
the minimal total area? Observe that the arrangement is completely determined
by *R *. Before looking at the solution
try to solve the problem on your own. Simple trigonometry should allow
you to determine the length of the line segment from the centre of the
triangle to the midpoint of a side. Once you have this, the rest of the
geometry is quite simple.

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*Instructor*

*Mike Zabrocki*

*Email address: zabrocki@yorku.ca*

*Department of Mathematics and Statistics*

*York University*

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