Pythagoras Variation Bithagoras, Proof (en)
A right triangle ABC is given with = 90°, along with a point X inside the triangle. The feet of the perpendiculars from X divide the sides a, b, c into a1, a2, and b1, b2, and c1, c2. Squares are constructed on these segments. First, let X lie on side c = AB. Vary X in such a way that c1 and c2 remain unchanged (e.g., using the up arrow key). Display the auxiliary triangles and use them to justify that a1² + a2² + b1² + b2² ≥ c1² + c2², and that equality holds precisely when X lies on c = AB.