9712
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Bisection of Segments by the Sides of a Triangle
Let ABC be a triangle with orthocenter H, and let the feet of the altitudes be A', B' and C'. Let the extensions of the altitudes intersect the circumcircle a second time at A'', B'', and C''. Then HA' = A' A'', HB' = B' B'', and HC' = C' C''.
Contributed by:
Jay Warendorff
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
See Theorem 178 in N. Altshiller-Court,
College Geometry
, 2nd ed., Mineola, NY: Dover, 2007 p. 95.
RELATED LINKS
Altitude
(
Wolfram
MathWorld
)
Circumcircle
(
Wolfram
MathWorld
)
Orthocenter
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Bisection of Segments by the Sides of a Triangle
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/BisectionOfSegmentsByTheSidesOfATriangle/
Contributed by:
Jay Warendorff
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
Bisecting a Line Segment through the Orthocenter
Jay Warendorff
Points Symmetric to the Orthocenter with Respect to the Sides of a Triangle
Jay Warendorff
A Concurrency Generated by Lines through the Orthocenter and Circles about a Triangle's Sides
Jay Warendorff
Circumradii Perpendicular to the Sides of the Orthic Triangle
Jay Warendorff
Line Segments through the Vertices and the Circumcenter of an Acute Triangle
Jay Warendorff
The Product of the Perpendiculars to the Sides of a Triangle
Jay Warendorff
A Line Parallel to a Side of a Triangle
Jay Warendorff
A Circumcircle through the Midpoint of a Triangle's Side
Jay Warendorff
Products of Segments of Altitudes
Jay Warendorff
Another Concurrency Generated by Circles about a Triangle's Sides and Lines through an Internal Point
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+