[size=150]Let ABC be a right-angled triangle with the right angle at C, and let X be a point inside the triangle (PointOn). [br]The feet of the perpendiculars from X divide the sides a, b, c into a[sub]1[/sub], a[sub]2[/sub], b[sub]1[/sub], b[sub]2[/sub], c[sub]1[/sub], c[sub]2[/sub].[br][list=1][br][*]Then the inequality a[sub]1[/sub]² + b[sub]1[/sub]² + a[sub]2[/sub]² + b[sub]2[/sub]² ≥ c[sub]1[/sub]² + c[sub]2[/sub]² holds. [br]Equality holds if and only if X lies on c = AB. [br]For X = A or X = B, we obtain the usual Pythagorean theorem.[/*][br][*]And the following equality holds: a[sub]1[/sub]² + b[sub]1[/sub]² + c[sub]1[/sub]² = a[sub]2[/sub]² + b[sub]2[/sub]² + c[sub]2[/sub]².[/*][/list][/size]