9722
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
1992 CMO Problem: Cocircular Orthocenters
Let
,
,
,
be distinct points on a circle (black) centered at
. Let
be the orthocenter of triangle
and so on. You can show that the four orthocenters are cocircular and the circle (green) has the same radius as the original circle.
Contributed by:
Shenghui Yang
THINGS TO TRY
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
This Demonstration is based on a problem from the 2nd Section of the Chinese Math Olympic National Final in 1992.
RELATED LINKS
Cyclic Quadrilateral
(
Wolfram
MathWorld
)
Orthocenter
(
Wolfram
MathWorld
)
PERMANENT CITATION
Shenghui Yang
"
1992 CMO Problem: Cocircular Orthocenters
"
http://demonstrations.wolfram.com/1992CMOProblemCocircularOrthocenters/
Wolfram Demonstrations Project
Published: June 18, 2012
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
Boltyanski's Cake Problem
Mikhail Skopenkov
A 2011 IMO Tangency Problem
Jay Warendorff
The Centroid, Circumcenter, and Orthocenter Are Collinear
Jaime Rangel-Mondragon
The Orthocenter of the Medial Triangle
Jay Warendorff
Collinearity of a Triangle's Circumcenter, Incenter, and the Contact Triangle's Orthocenter
Jay Warendorff
Collinear Orthocenters
Jay Warendorff
A Concurrency of Lines Joining Orthocenters
Jay Warendorff
The Malfatti Problem
Jaime Rangel-Mondragon
Cyclic Quadrilaterals, Subtriangles, and Incenters
Jay Warendorff
An IMO Problem Involving Concurrency
Jay Warendorff
Related Topics
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+