A Collinearity between the Nine-Point Center, the Foot of an Altitude, and a Midpoint
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Let ABC be a triangle with nine-point center N. Let B' be the foot of the altitude from B. Let the circumdiameter through B intersect AC at D. Let the midpoint of BD be M. Then M, N, and B' are collinear.
Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA
See problem 67 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 119.