I'm having a little bit of difficulty with these problems.
Looking for any kinds of advice/shortcuts that would enable me to solve these problems quicker.
Thanks

26.

never used the word "centroid" cause not native english, but...that point P divides each of the lines going through it in 2:1. so 2*PM = BP

2*(2*x + 5) = 7*x + 4
4*x + 10 = 7*x + 4
3*x = 6
x = 2
PM = 2*x + 5 = 9

8.

center of that circle is created by lines which divide the angles of the triangle on half, so basically AD = AE, BE = BF and CD = CF. so

AC = AD + DC = AE + CF = 12 + 15 = 27

no idea why they gave AB too

first question i cant help cause no idea about the words

Thanks !

Just need help on the first one, I don't know if there's any shortcuts to that.

well im bad with paperwork, but if the point where the medians meet is the same as where the altitudes meet, the triangle has all same sides if it means anything

;-; hmm

e: yeah i think it is

This post was edited by Sefira on May 22 2013 09:36pm

Indeed, since each median is the same as an altitude (2 common poi nts).

So they all are perpendicular bisectors. (A perpendicular bisector is a line that forms a right angle with one of the triangle's sides and intersects that side at its midpoint.)
And all points on the perpendicular bisectors are equidistant from two of the vertices of the triangle : any third vertices is equidistant from the 2 others !