What (not-so-obvious-at-first) geometry theorem is dynamically being illustrated here? [br](Feel free to move the gray vertices anywhere you'd like.)
[b]Theorem:[/b] [br][br]Suppose, in a right triangle, an [color=#980000][b]altitude[/b][/color], [color=#9900ff][b]median[/b][/color], and [color=#1e84cc][b]angle bisector[/b][/color] are drawn to its hypotenuse. Suppose [i]C[/i] is the vertex of the [b][color=#666666]right angle[/color][/b]. Then the [color=#1e84cc][b]bisector[/b][/color] of the [color=#666666][b]right angle[/b][/color] of this triangle [color=#ff00ff][b]bisects[/b][/color] the angle with vertex [i]C[/i] having sides of this described [color=#980000][b]altitude[/b][/color] and [color=#9900ff]median[/color].