Question

if a triangle is inscribed in a circle so that one of the triangle's sides is a diameter of the circle, what is the greatest area that the triangle can have in terms of the radius, r, of the circle?

Answer 1

Since the formula for the area of a triangle is 1/2 * base * height.

V = 1/2 b * h, in our case b = 2r - the diameter => V = r * h, and since h can only be between 0 and r => V = r^2