Set of all triangles with two equal edges inscribed in a circle. Let $\Delta$ be the set of all triangles with two equal edges inscribed in a circle of radius $R$.
So, how do I show that:
1,  The equilateral triangle in $\Delta$ is the one maximizing the area.
2, The equilateral triangle in $\Delta$ is the one maximizing the circumference?
Help greatly appreciated!

Say the angle between the two equal edges of the triangle is $\theta$. Can you work out the lengths of the edges as a function of $\theta$? Once you have the lengths of the edges can you find the area and perimeter (I'm assuming that's what you meant by circumference) with respect to $\theta$, and then maximize?
