Three Concyclic Sets of Points Associated with the Orthic Triangle
Three Concyclic Sets of Points Associated with the Orthic Triangle
Let ABC be an acute triangle and H its orthocenter. Let A', B', and C' be the feet of the altitudes from A, B, and C. Let L, M, and N be the contact points of the orthic triangle with its incircle with L on A'B', M on A'C', and N on B'C'. Then A', M, H, L are concyclic as are B', L, H, N and C', M, H, N.
Details
Details
The statement of the theorem is in Problem 136. Orthic Triangle, Altitudes, Orthocenter, Incenter, Perpendicular, Concyclic Points.
External Links
External Links
Permanent Citation
Permanent Citation
Jay Warendorff, Antonio Gutierrez
"Three Concyclic Sets of Points Associated with the Orthic Triangle"
http://demonstrations.wolfram.com/ThreeConcyclicSetsOfPointsAssociatedWithTheOrthicTriangle/
Wolfram Demonstrations Project
Published: March 7, 2011