A Triangle Formed by the Centers of Three Nine-Point Circles
Let ABC be a triangle and let A', B', and C' be the midpoints of BC, AC, and AB, respectively. Let A'', B'', and C'' be the centers of the nine-point circles of the triangles AB'C', BC'A', and CA'B', respectively. Then A''B''C'' is homothetic with ABC in the ratio 1:2.[more]
In the figure s(XY) is the slope of XY.[less]
See problem 72 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 120.
"A Triangle Formed by the Centers of Three Nine-Point Circles"
Wolfram Demonstrations Project
Published: March 7 2011