Angular Bisectors of a Rectangle

Proposed Problem 1

What is the figure formed by joining the four intersection points of the angular bisectors of the interior angles of a rectangle?






Conjecture

The figure formed by joining the four intersection points of the angular bisectors of the interior angles of a rectangle is a square.




Hint

A square is a quadrilateral with four equal sides and four right angles.

Please enable Java for an interactive construction (with Cinderella).
Drag free elements (free points A and B, or semi free point C) to alter the rectangle ABCD and observe the length of sides and the angles of the figure KLMN, which is formed by joining the intersection points of the angular bisectors of the interior angles of a rectangle to check the correctness of the made conjecture.