Newton line

In Euclidean geometry the Newton line is the line that connects the midpoints of the two diagonals in a convex quadrilateral with at most two parallel sides. The line segments and that connect the midpoints of opposite sides (the bimedians) of a convex quadrilateral intersect in a point that lies on the Newton line. This point K bisects the line segment that connects the diagonal midpoints. By Anne's theorem and its converse, any interior point P on the Newton line of a quadrilateral ABCD has the property that where [△ABP] denotes the area of triangle △ABP. If the quadrilateral is a tangential quadrilateral, then its incenter also lies on this line.