Extend the bisectors of angles A, B, and C of triangle ABC to meet the circumcircle at points X, Y, and Z. Show that I is the orthocenter of triangle ABC.

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- Mar 9th 2009, 08:11 AMtrojanlaxx223Geometry help.
Extend the bisectors of angles A, B, and C of triangle ABC to meet the circumcircle at points X, Y, and Z. Show that I is the orthocenter of triangle ABC.

- Mar 9th 2009, 08:54 AMred_dog
I think I is the orthocenter of XYZ. (not ABC)

Let

Then,

In the same way