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.
After work by:
THINGS TO TRY
D. Grinberg, "From Baltic Way to Feuerbach: A Geometrical Excursion,"
(2), 2000 p. 2.
Four Concyclic Points
Wolfram Demonstrations Project
Published: April 2, 2008
Embed Interactive Demonstration
More details »
Download Demonstration as CDF »
Download Author Code »
More by Author
An Altitude and Four Concyclic Points
Concyclic Points Derived from Midpoints of Altitudes
Concyclic Points Associated with an Angle Bisector and an Excircle
Concyclic Points from Reflections of the Circumcenter about the Altitudes
Concyclic Points Related to a Midpoint and the Incircle
Three Concyclic Sets of Points Associated with the Orthic Triangle
Four Collinear Points Related to the Altitudes
The Radii of Four Incircles
A Relation between Altitudes of Four Triangles
High School Geometry
High School Mathematics
Browse all topics
The #1 tool for creating Demonstrations
and anything technical.
Explore anything with the first
computational knowledge engine.
The web's most extensive
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
STEM Initiative »
Programs & resources for
educators, schools & students.
Join the initiative for modernizing
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
© 2016 Wolfram Demonstrations Project & Contributors |
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