Is it Possible to draw triangle where the orthocenter and the centroid of the triangle meet at the same point?

Question

Please HELP! And if this is possible could someone like tell me how to draw it? THX

Answer 1

He's right -- equalateral triangle is the only one.

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Answer 2

An equilateral triangle has that property -- all its centres coincide.
And, on further reflection, I realise it's the only sort of triangle that does this, because:
If the centroid (which is on the median) is the orthocentre (which is on the altitude), then the median must be the altitude, which makes it the perpendicular bisector of the side it's drawn to. That makes the triangle isosceles from the point of view of that side as base. But then it applies to every side, so the triangle must be equilateral.

Answer 3

Wouldn't that condition be satisfied only in an equilateral triangle? You know, three 60-degree angles and three identical sides. This is a very faint old memory, so don't bet the farm on it!