# Middle of triangles

I need an engine that can get the middle of a triangle

There are about five different things that you can mean by "middle." Do you mean the point of intersection of the angle bisectors, the point of intersection of the perpendicular bisectors of the sides, the point of intersection of the lines connecting each vertex to the midpoint of the opposite side, the point that minimizes the sum of the distances from that point to the three sides, the center of mass (the point around which you can balance the triangle on a sharp point), umm, did I forget any? I think each of those last two might be the same point as one of the first three, but it's been a long time since I took geometry.

"the center of mass" is exactly "the point of intersection of the lines connecting each vertex to the midpoint of the opposite side", and you missed the point of intersection of the three altitudes.
I'm a student preparing for mathematical olympiads, so I know them.

Cut him some slack

I have a block for drawing a regular polygone around the center of the mass.

project

Good luck!

Well it depends on what kind of triangle it is. Is it an equilateral triangle? Is it an isosceles triangle?

if you know the coordonates of the 3 points (?? i don't know how to tell it in english)

you can calculate the average of the 3 points...

for the x (3+4+1)/3 = 8/3
for the y (5+1+0)/3 = 3

in this case: (2.666666 , 2)

(Please forgive my past self; I don't know what he was thinking.
None of us understood each other or me.)

polygon, coordinates, "I" by itself and the "E" in "English" are usually capitalized

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I need an engine that can get the middle of a triangle