Hi (please help)

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my doctor give me this chalnge problmes


Find the dimensions of the isoseceles tringale of least area that circumscribes a circle of raduios r
 

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HallsofIvy
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my doctor give me this chalnge problmes


Find the dimensions of the isoseceles tringale of least area that circumscribes a circle of raduios r
Your doctor prescribed this?
(That's a joke- in the United States at least "Doctor" is almost always interpreted as "Physician".)

But it does mean that this should go in the homework section so I'm going to move it.

The first thing I would do is draw a picture. Can you show, by symmetry, perhaps, that such an isosceles triangle must be an equilateral triangle? And hopefully recognise that the center of the circle is at the point where the altitudes of the triangle intersect. Now, do you know a relation between the length of the sides of an equilateral triangle and the length of an altitude? And a relation between the entire length of the altitude and the length from the intersection of altitudes to the foot of an altitude?
 

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