Thread: Is the orthocenter so named cuz it's the incenter of the orthotriangle of a triangle?

Why is the orthocenter named orthocenter? I know it's the intersection of the altitudes of a triangle but I'm guessing the reason why it's called orthocenter is because it's the incenter of the orthotriangle of a triangle.

Originally Posted by lamp23

Why is the orthocenter named orthocenter? I know it's the intersection of the altitudes of a triangle but I'm guessing the reason why it's called orthocenter is because it's the incenter of the orthotriangle of a triangle.

Maybe this helps:

1. The "trace" of an orthogonal projection of a vertex of a triangle "down" to the base is called height of the triangle. (Compare Altitude (triangle) - Wikipedia, the free encyclopedia).

2. The orthocenter is the intersection of these "traces" as you've stated correctly.

3. If you use the meaning of the word: ortho means right, gonos means vertex, so "orthogonal" means "of a right angled vertex".

doesn't gonos mean angle? which makes more sense by the way. but your explanation wouldn't explain why it's called the orthocenter

Originally Posted by lamp23

doesn't gonos mean angle? which makes more sense by the way. but your explanation wouldn't explain why it's called the orthocenter

If you follow the link, you will see that it is indeed the center of an incircle of a triangle.

Right, I knew it was. I wanted to make sure that its namesake came from that center and not some other one.