what's the difference between orthocenters, circumcenters, and any other kind of center? i'm supposed to already know this, but i don't remember learning it. it's not an emergency, but i would like someone to explain the difference and a good way to remember them. thanks :)

Question

anonymous · Answer

I didn't know these either :( I'm reading about them here: http://www.vitutor.com/geometry/plane/orthocenter.html

aripotta · Answer

it's just so confusing :(

aripotta · Answer

how am i supposed to remember these?

anonymous · Answer

That site wasn't very good, and yes, it does seem confusing... probably why I didn't remember ever learning these :( Here's a different site for orthocenter: http://easycalculation.com/analytical/orthocenter-triangle.php

aripotta · Answer

i think i got incenter and circumcenter down. i remember having to construct circles around and in triangles

anonymous · Answer

You should be able to construct the orthocenter in a triangle also... need perp lines from each side to the opposite vertices.

anonymous · Answer

That diagram at that second link showed it less confusingly, I thought...

aripotta · Answer

are the perpendicular lines also angle bisectors?

anonymous · Answer

no, it appears that is the difference between orthocenter and circumcenter

aripotta · Answer

ugh.

anonymous · Answer

Well, if you were trying for a memory technique, this one isn't perfect but maybe it will help.

"Ortho" usually means perpendicular... like "orthogonal" is more or less the same thing as perpendicular (don't worry about the details now).

So an ortho-center is found by the intersection of perpendicular lines from the vertices.

A circumcenter (unfortunately) also uses perp lines, but that uses the angle bisectors.

So:  "Ortho"    ----> perp lines only.... 
      "Circum"   ---> angle bisectors  (but also perp)

aripotta · Answer

i usually think of bones when i hear ortho :l

anonymous · Answer

ortho in math, not in medicine...  same word, but different meaning for different disciplines.

I said it wasn't a great memory technique, didn't I?  :)

aripotta · Answer

oh wait and orthodontist is a dentist lol

aripotta · Answer

an*

aripotta · Answer

alright, i'll try to use that. thanks :)

anonymous · Answer

Lots of time, the dumber the memory-jogger, the better it works :)