Prove that triangle is equilateral

Question

I have a triangle here, how do I prove that $BCD$ is equilateral(so all lines have the same length)

And yes this is 2D

What I have so far is $$BAC = 120^\circ$$

So how do I point out that $$BCD = 60^\circ$$ $$CBD = 60^\circ$$ $$BDC = 60^\circ$$ Where is the relationship ?

Answer 1

Angle BAD and angle BCD share the chord in the right way, so they are equal. The same for angle CAD and angle CBD. This gives us two angles of the triangle BCD equal to 60 degrees, so that's it.

Answer 2

c = 120 due inscribed angle BAD. in the same way arc CD = c

so, CBD = BCD which is 60.

in the same way as arc CB = 240 and arc CB = 120. CDB = 60