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Newton line
In Euclidean geometry the Newton line is the line that connects the midpoints of the two diagonals in a convex quadrilateral other than a parallelogram.
The line segments GH and IJ 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 EF 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.
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Newton line AI simulator
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Newton line
In Euclidean geometry the Newton line is the line that connects the midpoints of the two diagonals in a convex quadrilateral other than a parallelogram.
The line segments GH and IJ 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 EF 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.