- 1. The Circle which passes through the feet of the Perpendiculars dropped from the
Vertices of any Triangle on the sides opposite them passes also through the
Midpoints of these sides as well as through the Midpoint of the segments which join the
Vertices to the point of intersection of the Perpendicular (a Nine-Point
- 2. The Nine-Point Circle of any Triangle is Tangent internally to the Incircle and
Tangent externally to the three Excircles.
See also Excircle, Feuerbach Point, Incircle, Midpoint, Nine-Point Circle, Perpendicular,
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 117-119, 1967.
Dixon, R. Mathographics. New York: Dover, p. 59, 1991.
© 1996-9 Eric W. Weisstein