I have to solve the following problem:
Consider an equilateral triangle $ABC$ and $\mathcal{C}$ its circumscribed circle. Let $M$ be a point located on the arc of the circle defined by $[AC]$ which does not contain $B$.
1) Show that $BM$ is the bisector of the angle $\widehat{AMC}$.
2) Let $D$ be a point of $[BM]$ such that $DM=DA$. Show that the triangle $DAM$ is equilateral.
3) Show: $MA + MC = MB$.
I was able to prove 1) and 2), but I am stuck at 3). Can anyone help me with point 3). Thank you in advance!