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Three Equal Segments from the Altitudes of a Triangle
In the triangle
let the feet of the altitudes be
,
, and
. The circle with diameter
meets
and
at two points other than
to form a segment of length
; similarly define
and
. Prove that
.
Contributed by:
Jaime Rangel-Mondragon
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The segments of equal length are drawn in blue.
This Demonstration comes from problem 19 of the shortlisted problems for the
1971 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. 73.
PERMANENT CITATION
Jaime Rangel-Mondragon
"
Three Equal Segments from the Altitudes of a Triangle
"
http://demonstrations.wolfram.com/ThreeEqualSegmentsFromTheAltitudesOfATriangle/
Wolfram Demonstrations Project
Published: July 11, 2013
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