How to detect the equilateral triangle from the given triangle?

I’m struggling to fit the given triangle below to the equilateral triangle.
I have no clue how to detect it. I just want the three points that represents he equilateral triangle.

Thanks a lot for advising.

It looks like as an exercise.
What have you already done?
There are many tutorials about contour OpenCV: Image Processing (imgproc module) may be one will help you to solve your problem