Newton line
E, K, F lie on a common line, the 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.[1]
This line has a few interesting geometrical properties. In particular, the line segments connecting the midpoints of opposite sides of a convex quadrilateral intersect in a point that lies on the Newton line. If the quadrilateral is a tangential quadrilateral, then its incenter also lies on this line.[2]
See also
References
- ↑ Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics. MAA, 2010, ISBN 9780883853481, pp. 108-109 (online copy, p. 108, at Google Books)
- ↑ Dušan Djukić, Vladimir Janković, Ivan Matić, Nikola Petrović, The IMO Compendium, Springer, 2006, p. 15.
External links
- Weisstein, Eric W., "Léon Anne's Theorem", MathWorld.
- Cut the knot