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Circumcircles of Two Midpoints and an Altitude
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
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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
Jaime Rangel-Mondragon
"
Circumcircles of Two Midpoints and an Altitude
"
http://demonstrations.wolfram.com/CircumcirclesOfTwoMidpointsAndAnAltitude/
Wolfram Demonstrations Project
Published: July 11, 2013
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