A Triangle Formed by the Centers of Three Nine-Point Circles

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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]
Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
See problem 72 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 120.
Permanent Citation
"A Triangle Formed by the Centers of Three Nine-Point Circles"
http://demonstrations.wolfram.com/ATriangleFormedByTheCentersOfThreeNinePointCircles/
Wolfram Demonstrations Project
Published: March 7 2011