Concyclic Points Derived from Midpoints of Altitudes

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Let ABC be a triangle and D, E, F be the feet of the altitudes. Let D', E', F' be the midpoints of the segments AD, BE, CF. Let the line E' F' meet the lines AB and CA at the points B' and C'', let the line F'D' meet the lines BC and AB at the points C' and A'', and let the line D'E' meet the lines CA and BC at the points A' and B''. If X, Y, Z are the circumcenters of triangles AB'C'', BC'A'', and CA'B'', respectively, then the points D', E', F', X, Y, Z are concyclic.

Contributed by: Jay Warendorff (March 2011)
After work by: A. Angelescu
Open content licensed under CC BY-NC-SA


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.