Computing the coordinate of an equilateral triangle

Question

I have this triangle, all that I know are its sides length and that the center is at x,y = 0,0 of the 2D plan.

How do I compute the (x, y) coordinate the points A,B,C?

(h1, h2 and l1 are not know, they are on the pictures because I also want to compute them, it's not in the title but if you also know how to compute them I'm all hears :p)

This is to draw something with triangles with python in blender, being unable to find the right geometry tool to compute those values I drawed the triangle on paper and took some measurments, however the precision error of my ruler adds up after several iterations, making a mess.

Thanks.

Answer 1

HINT

Recall that

• $h=h_1+h_2=\frac{\sqrt 3}2T$
• $h_2=2h_1$

Answer 2

Alternatively, the point $(0,0)$ is both incenter and circumcenter, thus: $$r=h_1=\frac{S}{p}=\frac{\frac{\sqrt{3}}{4}T^2}{\frac{3T}{2}}=\frac{T}{2\sqrt{3}};\\ R=h_2=\frac{abc}{4S}=\frac{T^3}{4\cdot \frac{\sqrt{3}T^2}{4}}=\frac{T}{\sqrt{3}}.$$