11159
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
THINGS TO TRY
Drag Locators
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
Jaime Rangel-Mondragon
"
Circumcircles of Two Midpoints and an Altitude
"
http://demonstrations.wolfram.com/CircumcirclesOfTwoMidpointsAndAnAltitude/
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
Three Equal Segments from the Altitudes of a Triangle
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
A Triangle Inequality Involving the Altitudes, Semiperimeter, Inradius, and Circumradius
Jay Warendorff
Bisecting the Area and Perimeter of a Triangle
Jaime Rangel-Mondragon
Squares on a Line Segment
Jaime Rangel-Mondragon
Four Lines and Four Circumcircles
Jaime Rangel-Mondragon
The Intersection of Two Triangles
Jaime Rangel-Mondragon
An IMO Triangle Problem
Oleksandr Pavlyk
Two-by-Two Linear Systems Problem Generator
Bruce Torrence
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+