Question

prove that the centroid of a scalene triangle divides the line joining orthocenter and circumcenter in the ratio 2:1

Answer 1

Ewwww geometry.

That is all.

Answer 2

cant apply anythng here.........

Answer 3

The Euler Line of the triangle starts at the circumcenter, goes through the centroid, to the orthocenter... It's a start.

Answer 4

Lol at that being a start..

Answer 5

wtf........jas cant read ur minds

Answer 6

It's apparently a purely geometric proof.
http://planetmath.org/encyclopedia/EulerLineProof.html

Answer 7

You thought it was going to be something other than geometric...?

Answer 8

I was hopeful...

Answer 9

If I had formulas for centroid, orthocenter, and circumcenter of a scalene triangle based upon the vertexes, I could in theory show the ratio of the distances is always 1/2.

Answer 10

No, you couldn't.

Regardless of whether it is possible, YOU couldn't do it.

Answer 11

Ouch...

Answer 12

You're welcome.

Answer 13

I didn't see the need to be degrading. I am simply here to try to help.

Answer 14

Just joshin', no need to call a wambulance :(

Answer 15

this is what I have so far, since there is no restrictions to define a scalene other than different angles/side lenths...a right scalene should prove it just as well.... i used the 3-4-5

Answer 16

if I could prove that the line bisects the hypot at a right angle, its solved lol

Answer 17

Unfortunately, I think proof need to be more general than 'it works for a RA with these sides => it works for all'

But I hate geometry, so meh.

Answer 18

feeling sleepy....c u guys later

Answer 19

thats true, proofs need to be more rigorous, but I aint to good with that part ;)

Answer 20

I am. When there's no drawing involved.

Answer 21

I get congruent triangles like this..... but is there a theorum which states that the apex of a triangle within an rectangle has a ratio of sides equal to the distance between the 2 top corners?

Answer 22

Since we have 2 congruent triangles with equal angles A and B, then the ration of 50/3 sinB would match 25/3 sinB to be true.

Answer 23

got it!!