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.


Mike Zabrocki
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Department of Mathematics and Statistics
York University
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