Quadrilateral - Other Properties of Convex Quadrilaterals

Other Properties of Convex Quadrilaterals

• Let exterior squares be drawn on all sides of a quadrilateral. The segments connecting the centers of opposite squares are (a) equal in length, and (b) perpendicular. Thus these centers are the vertices of an orthodiagonal quadrilateral. This is called Van Aubel's theorem.
• The internal angle bisectors of a convex quadrilateral either form a cyclic quadrilateral or they are concurrent. In the latter case the quadrilateral is a tangential quadrilateral.
• For any simple quadrilateral with given edge lengths, there is a cyclic quadrilateral with the same edge lengths.