Challenge Your Geometry Skills with Problem 1456: Altitudes, Orthic Triangle, Circumcircle, Parallel, Similarity, and Area

Let AHA, BHB, CHC be the altitudes of triangle ABC. The extensions of AHA, BHB, and CHC intersect the circumcircle O at A1, B1, and C1, respectively. Prove that (1) HAHB // A1B1, HBHC // B1C1, and HAHC // A1C1; (2) the area of triangle A1B1C1 is 4 times the area of triangle HAHBHC.

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Static Diagram of problem 1456

Dynamic Geometry 1456: Altitude, Orthic Triangle, Circumcircle, Similarity, Area. Using GeoGebra


Poster of the problem 1456 using iPad Apps

Poster of Problem 1456, Altitude, Orthic Triangle, Circumcircle, Similarity, Area. Using iPad

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Geometry Problem 1456 Solution(s)