Can someone list all the important points inside a triangle (and briefly describe what they are) which are found using the perpendiculars at midpoint of sides etc. e.g. centroid

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Can someone list all the important points inside a triangle (and briefly describe what they are) which are found using the perpendiculars at midpoint of sides etc. e.g. centroid

Mathematics
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centroid-----intersection of medians incenter----- intersection of internal angle bisectors circumcenter ---intersection of perpendicular bisectors of sides
is that all? I thought there were more
and there is one more...orthocenter---intersection of altitudes

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OK. do you know how to prove these are are collinear? (e.g. using coordinate geom)
yes...you can prove
can you help? Please :D
|dw:1347448272061:dw|
prove centroid, orthocenter and circumcenter are collinear
i have taken the coordinate of A=(1,0) for simplicity
Yep
now find the centroid...
u know to find the centroid if coordinate of vertices of a triangle are given...
not really
http://mathforum.org/library/drmath/view/57665.html
http://www.vitutor.com/geometry/plane/orthocenter.html
Don't worry found it in my text book. Thanks anyway
http://www.askiitians.com/iit_jee-Straight_Line/Centroid_Incentre_and_Circum_Centre
open this one...you'll get...how to calculate centroid, inceter...
http://www.askiitians.com/iit_jee-Straight_Line/Centroid_Incentre_and_Circum_Centre this is useful one.
I'm getting an error opening that one. If its really useful, would you be so kind to save it as a pdf and attach it

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