A right triangle is inscribed in a circle with a diameter 100 units long. What is the maximum area of the triangle, in square units?
The largest triangle, by area, that can be inscribed in a triangle is the equilateral triangle. Since you need a right triangle, you can swing one of the points to the other, which gives you a 30-60-90 triangle, with sides 50, 50*sqrt(30), and 100. The area of this triangle is 1/2*50*50*sqrt(3) = 1250*sqrt(3).