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

Question

anonymous · Answer

centroid-----intersection of medians
incenter----- intersection of internal angle bisectors
circumcenter ---intersection of perpendicular bisectors of sides

anonymous · Answer

is that all? I thought there were more

anonymous · Answer

and there is one more...orthocenter---intersection of altitudes

anonymous · Answer

OK. do you know how to prove these are are collinear? (e.g. using coordinate geom)

anonymous · Answer

yes...you can prove

anonymous · Answer

can you help? Please :D

anonymous · Answer

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anonymous · Answer

prove centroid, orthocenter and circumcenter are collinear

anonymous · Answer

i have taken the coordinate of A=(1,0) for simplicity

anonymous · Answer

Yep

anonymous · Answer

now find the centroid...

anonymous · Answer

u know to find the centroid if coordinate of vertices of a triangle are given...

anonymous · Answer

not really

anonymous · Answer

http://mathforum.org/library/drmath/view/57665.html

anonymous · Answer

http://www.vitutor.com/geometry/plane/orthocenter.html

anonymous · Answer

Don't worry found it in my text book. Thanks anyway

anonymous · Answer

http://www.askiitians.com/iit_jee-Straight_Line/Centroid_Incentre_and_Circum_Centre

anonymous · Answer

open this one...you'll get...how to calculate centroid, inceter...

anonymous · Answer

http://www.askiitians.com/iit_jee-Straight_Line/Centroid_Incentre_and_Circum_Centre this is useful one.

anonymous · Answer

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

anonymous · Answer

@akash123