Question

For what kind of triangle is the centroid located outside of the triangle? Explain.

Or is it that it's not possible?

Answer 1

Please define "Centroid".

Answer 2

The point at which the tree medians of a triangle concur.

Answer 3

three*

Answer 4

Okay. Please define "Median".

Answer 5

A segment that bisects a segment into two equal parts.

Answer 6

Okay, so we have three perpendicular bisectors. By a wonderful miracle of geometry, they intersect in the same point. The question is, will this point ALWAYS be inside the triangle?

Try a really funny triangle and see. Do an isosceles triangle with angles 170º, 5º, and 5º. I dare you to get the Centroid inside the triangle. :-)

Answer 7

Too much work :( I'm too lazy.

Answer 8

Then try 120º, 30º, 30º. Inside or out? Your drawing will have to be better for this one. That first one, even laxy people can see it.

Answer 9

Not possible

Answer 10

Fine, I'll do it.

Answer 11

@tkhunny no matter what, centroid lies inside a triangle.

Answer 12

@tkhunny i think you are taking perpendicular bisectors. That is different from a median

Answer 13

I would be surprised if centroid (center of gravity can be outside
the triangle. Run lines from vertices to mid-side opposite each vertex to find center of gravity, which I think is "centroid." If they are equivalent, the centroid will not be outside the triangle, even for 5, 170, 5 nearly flat one. All the lines I have just described will be within the triangle, as must their intersection. Handbook says area centroid for triangle is intersection of medians, which I believe is what I am describing.

Answer 14

"A segment that bisects a segment into two equal parts."

That's not really clear, is it?

Yes, I was using perpendicular bisectors. This leads to the CircumCenter, not the Centroid.

"A segment that CONNECTS a vertex to the opposite side AND bisects the opposite side." Oh, the Median!!

Too lazy to provide a good definition. I trusted you.
Too lazy to notice that I thought you did your homework and agreed that it was the perpendicular bisector.

New plan, listen to @pratyush5 :-)

Answer 15

Okay, but I was the one asking for help. And I was the one trusting you. Don't blame me, I just don't want to measure out the triangles. It's a simple yes or no question. Thanks anyway.

Answer 16

You do better and I'll go take a nap so I don't make any more errors, today.

It's never a simple question. It's learning.

Answer 17

Learned a whole lot with just the answer "Not possible" by @pratyush5.

Answer 18

Helped me twice in a row :) You're awesome.