Circumcircles of Two Midpoints and an Altitude

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
In the triangle let
and
be the midpoints of the sides
and
and let
be the foot of the altitude from
to
. Prove that the circumcircles of the triangles
,
, and
have a common point
and that the line
passes through the midpoint of the segment
.
Contributed by: Jaime Rangel-Mondragon (July 2013)
Open content licensed under CC BY-NC-SA
Snapshots
Details
This Demonstration comes from problem 6 of the shortlisted problems for the 1970 International Mathematical Olympiad (IMO).
Reference
[1] D. Djukić, V. Janković, I. Matić, and N. Petrović, The IMO Compendium, 2nd ed., New York: Springer, 2011 p. 69.
Permanent Citation
"Circumcircles of Two Midpoints and an Altitude"
http://demonstrations.wolfram.com/CircumcirclesOfTwoMidpointsAndAnAltitude/
Wolfram Demonstrations Project
Published: July 11 2013