## apple_pi 3 years ago 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

1. akash123

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

2. apple_pi

is that all? I thought there were more

3. akash123

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

4. apple_pi

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

5. akash123

yes...you can prove

6. apple_pi

7. akash123

|dw:1347448272061:dw|

8. akash123

prove centroid, orthocenter and circumcenter are collinear

9. akash123

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

10. apple_pi

Yep

11. akash123

now find the centroid...

12. akash123

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

13. apple_pi

not really

14. akash123
15. akash123
16. apple_pi

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

17. akash123
18. akash123

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

19. akash123
20. apple_pi

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

21. apple_pi

@akash123