Prove that all the inscribed angles are equal

Question

Consider a circunference that contains 3 inscribed angles which are opposite to the same arc

Prove that all the angles are equal. (See image for detail)

https://i.stack.imgur.com/5Wz3Y.png

Answer 1

A central angle is equal to the arc it is facing (for example if $O$ is the center of a circle and $A$, $B$ are 2 points on the circle, then $\widehat{AOB}=\overset{\frown} {AB}$

Now consider a third point $C$ on the circle and now what we want to prove is that $\widehat {ABC} = \frac{1}{2} \overset{\frown} {AB}$

Consider the triangles $ACO$ and $ABO$ and trying proving what is required to prove, can you do it now? Try and show your work please.

Check this video for a detailed proof.