An isosceles triangle is inscribed in a circle with radius one metre in such a way as to
maximize the area of the triangle. Determine its area. (Hint: Consider the area as a
function of the distance from the centre of the circle to the base of the triangle)
If the distance to the base from the center of the circle is r, then the height of the triangle is since the radius of the circle is 1 and we assume that all corners of the triangle touch the circle. All the corners of the triangle will be at the distance r=1 from the center of the circle, so the base is going to have the length
So we have