There is a triangle ABC, and there are 3 equilateral triangles such that each side of ABC is the base of one equilateral triangle, and the equilateral triangles are facing outwards(is not overlapping ABC).

Prove that the centers of each equilateral triangle together form another equilateral triangle.

Took me hours to solve this.

SparklingWater2 Aug 20, 2021

#1**+1 **

There is a triangle ABC, and there are 3 equilateral triangles such that each side of ABC is the base of one equilateral triangle, and the equilateral triangles are facing outwards(is not overlapping ABC).

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I didn't know this.

civonamzuk Aug 20, 2021

#2**+1 **

It's one thing to be able to draw it, and it's another to prove it using words :)

SparklingWater2 Aug 20, 2021

#3**0 **

Hi SparklingWater2

If it took you hours to solve it, then I guess you already have the answers.

So... you have posted it as an interest question?

That is perfectly fine but you should make it very clear that that is what you have done.

Melody Aug 21, 2021

#4**0 **

I agree SparlingWater2, this is a tricky problem.

I made an interactive pic here. (just because I like drawing pics with GeoGebra)

https://www.geogebra.org/classic/xfd4hxpf

No proof is jumping out at me. I will think about it more yet.

Do you intend to post your proof when people give up?

Melody Aug 21, 2021

#5**+1 **

Yes I do, and sorry about not mentioning the fact that this is answered. I will wait one or two more days, and see if anyone comes up with an answer :)

hint: similar triangles

SparklingWater2
Aug 21, 2021