Who is the orthic triangle similar to?

(I did this (10th finished) on Nov.14&16, 2009)

Chen Tian



I am gonna work on thefollowing interesting problem: Examine the triangle formed by the points where the extended altitudes meet the circumcircle. How is it related to the Orthic triangle? Proof? Will the relationship still hold if the original triangle is obtuse?

Check out the GSP sketch I made to manipulate, first.

Here is the case when the original triangle is acute.


Look! We get extra bonus:


But, unfortunately, the result does not hold when the original triangle is obtuse. See one conterexample below.


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