Let G denote the centroid of triangle ABC. If triangle ABG is equilateral with side length 2, then determine the perimeter of triangle ABC.

Question

I drew the diagram, but it doesn't really help....

Answer 1

Are you by any chance enrolled (or were enrolled) in AoPS Intro to Geometry course? Because I recognize all of the problems you post...

Answer 2

We have banned you from taking anymore AoPS. We can track your IP address.

Answer 3

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Answer 4

@AoPS Only AoPS impersonators "ban" people from taking AoPS. If a mod/teacher doesn't want you posting on other websites, they would simply tell you to use the message board.

Answer 5

You know that the sides of ABG are all 2. Then, since the centroid is the point of intersection of the medians, median CD which intersects line AB would create two equal lengths; AD=BD=1.

Then, because it is equilateral, <GBA=<GAB=<BGA=60 degrees, so the median would split <BGA in half, so <BGD=30 degrees. Because the sum of a triangle's interior angles is 180 degrees, triangle BGD is a right triangle, so length GD=sqrt(3).

Furthermore, you know that the centroid divides up medians into a ratio of 2:1, so CG=2sqrt(3).

I think you can figure the rest out.

Answer 6

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Answer 7

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Answer 8

"We have banned you from taking anymore AoPS. We can track your IP address." ...3 MONTHS LATER... AoPS says: "AoPS Admin and AoPS User, we appreciate that you are trying to stop people from cheating on AoPS homework, but unfortunately, no, we cannot track your IP address, nor do we care to do so."

Answer 9

@ The first person Anonymous, if you recognize the question from AoPs, doesn't that make you cheating too???