11087
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Circumcircles of Two Midpoints and an Altitude
Jaime Rangel-Mondragon
Three Circles with Two Common Tangents
Jaime Rangel-Mondragón
Reflections of a Line through the Orthocenter in the Sides of an Acute Triangle
Jaime Rangel-Mondragon
Bisecting the Area and Perimeter of a Triangle
Jaime Rangel-Mondragon
A Triangle Inequality Involving the Altitudes, Semiperimeter, Inradius, and Circumradius
Jay Warendorff
Squares on a Line Segment
Jaime Rangel-Mondragon
An IMO Triangle Problem
Oleksandr Pavlyk
Bisecting a Triangle
Jaime Rangel-Mondragon
Inscribe a Scaled Copy of a Triangle in Another Triangle
Jaime Rangel-Mondragon
Construction for Three Vectors with Sum Zero
Izidor Hafner
Related Topics
Mathematics Problems
Plane Geometry
Triangles
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+