Geometry, Theorems and Problems

Geometry Problem 1232: Triangle, Altitudes, Orthic Triangle, Collinearity, Orthic Axis. Tiled background image: Intihuatana, Machu Picchu. Level: College, High School.

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The figure shows a triangle ABC with the altitudes AA1, BB1, and CC1. CB and B1C1 extended meet at A2, AC and C1A1 extended meet at B2, AB and B1A1 extended meet at C2. Prove that points A2, C2, and B2 are collinear on a line called Orthic Axes.
Note: The triangle A1B1C1 is called the orthic triangle of the triangle ABC.
 

Geometry Problem 1232: Triangle, Altitudes, Orthic Triangle, Collinearity, Orthic Axis.

 

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Last updated: Jul 8, 2016