the problem is one of creating a right triangle using the diameter as the horizontal side and letting the other two sides (hypotenuse and the vertical side equal half the circumference = Pi if radius = 1). The question is: is that possible? I think the answer is no.
I calculated that you can't create a right triangle with
radius=1,
base = 2r,
height = r
and have the hypotenuse and the vertical side sum to pi. I would like to know if I was wrong or not.
You are very right it is just not possible. the reason is if one side is of right triangle is of length 2r ( diameter ) and other r 9 radius ) the hypotenuse will definitely be greater than the diameter and so will take the third vertex outside the circle.