[size=150]A right triangle ABC is given with[math]\gamma[/math]=[color=#cc0000] 90°[/color], along with a point [color=#6aa84f]X[/color] inside the triangle. [br]The perpendicular feet 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], and c[sub]1[/sub], c[sub]2[/sub]. [br]Squares are constructed on these segments. [br]The areas of the squares on the legs are added together (blue), as are the areas of the [br]squares on the hypotenuse (violet).[br]Drag [color=#6aa84f]X [/color]and compare the sums of the areas. Can you find a general statement? [br]In which case does equality hold? [br]For which position of [color=#6aa84f]X[/color] do we obtain the well-known Pythagorean figure? [/size]