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.

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- March 29th 2012, 10:21 AMlamp23Is 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.

- March 29th 2012, 10:39 AMearbothRe: Is the orthocenter so named cuz it's the incenter of the orthotriangle of a trian
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". - March 29th 2012, 11:37 AMlamp23Re: Is the orthocenter so named cuz it's the incenter of the orthotriangle of a trian
doesn't gonos mean angle? which makes more sense by the way. but your explanation wouldn't explain why it's called the ortho

**center** - March 29th 2012, 12:28 PMPlatoRe: Is the orthocenter so named cuz it's the incenter of the orthotriangle of a trian
If you follow the link, you will see that it is indeed the center of an incircle of a triangle.

- March 29th 2012, 01:36 PMlamp23Re: Is the orthocenter so named cuz it's the incenter of the orthotriangle of a trian
Right, I knew it was. I wanted to make sure that its namesake came from that center and not some other one.