Bithagoras Theorem (H.-J. Elschenbroich) (en)
Let ABC be a right-angled triangle with the right angle at C, and let X be a point inside the triangle (PointOn).
The feet of the perpendiculars from X divide the sides a, b, c into a1, a2, b1, b2, c1, c2.
- Then the inequality a1² + b1² + a2² + b2² ≥ c1² + c2² holds. Equality holds if and only if X lies on c = AB. For X = A or X = B, we obtain the usual Pythagorean theorem.
- And the following equality holds: a1² + b1² + c1² = a2² + b2² + c2².