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Math Help - Is the orthocenter so named cuz it's the incenter of the orthotriangle of a triangle?

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    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.
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    Re: Is the orthocenter so named cuz it's the incenter of the orthotriangle of a trian

    Quote Originally Posted by lamp23 View Post
    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".
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    Re: 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 orthocenter
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    Re: Is the orthocenter so named cuz it's the incenter of the orthotriangle of a trian

    Quote Originally Posted by lamp23 View Post
    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.
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    Re: 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.
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