Originally Posted by

**TimsBobby2** Let I_{a}, I_{b}, I_{c}, be the excenters of triangle ABC. Prove that A, B, and C are the feet of the altitudes of triangle I_{a}I_{b}I_{c} and that the incenter I of triangle ABC is the orthocenter of triangle I_{a}I_{b}I_{c. }

It seems obvious to me that once you show that A, B, and C are the feets of the altitudes of the triangle joining the excenters of triangle ABC that the incenter I of triangle ABC is the orthocenter of the other triangle because they are concurrent inside triangle ABC. However, how would I show that A, B, and C are the feet of the altitudes? Any help would be appreciated.