10075
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Four Concyclic Points
Let ABC be a triangle and H the foot of the altitude from B. Let M be the midpoint of AC. Let P and Q be the feet of the perpendiculars from A and C to the angle bisector of the angle ABC. Then H, M, P and Q lie on a circle.
Contributed by:
Jay Warendorff
After work by:
D. Grinberg
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
D. Grinberg, "From Baltic Way to Feuerbach: A Geometrical Excursion,"
Mathematical Refections
(2), 2000 p. 2.
RELATED LINKS
Circle
(
Wolfram
MathWorld
)
Concyclic
(
Wolfram
MathWorld
)
PERMANENT CITATION
Jay Warendorff
"
Four Concyclic Points
"
http://demonstrations.wolfram.com/FourConcyclicPoints/
Wolfram Demonstrations Project
Published: April 2, 2008
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
An Altitude and Four Concyclic Points
Jay Warendorff
Concyclic Points Derived from Midpoints of Altitudes
Jay Warendorff
Concyclic Points Associated with an Angle Bisector and an Excircle
Jay Warendorff
Concyclic Points from Reflections of the Circumcenter about the Altitudes
Jay Warendorff
Concyclic Points Related to a Midpoint and the Incircle
Jay Warendorff
Three Concyclic Sets of Points Associated with the Orthic Triangle
Jay Warendorff
Four Collinear Points Related to the Altitudes
Jay Warendorff
Concyclic Circumcenters
Jay Warendorff
The Radii of Four Incircles
Jay Warendorff
A Relation between Altitudes of Four Triangles
Jay Warendorff
Related Topics
Plane Geometry
Triangles
High School Geometry
High School Mathematics
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+