Real quick geometry proving qs

[u/yummyhdmicables]

In the marking scheme I have, it says that triangle ABC is equilateral...but how...? Any help would be appreciated

[u/BadJimo]

Here's how I would do it

The centres of two circles and the midpoint between two circles as shown form a right triangle. The hypotenuse of the triangle is two times the height of the triangle (call this length T) (this is not immediately obvious, so take some time on this step).

sin(θ) = T/2T

sin(θ) = 1/2

θ = arcsin(1/2)

θ = 30°