BD to AC to E

Because angle ABD= angle ACD=60 degrees

Triangle AEB is similar to triangle dec.

∠BAE=∠BDC

CE/BE=ED/EA

So △EBC∽△EAD

∠CBE=∠EAD ∠BCA=∠BDA

AB=AC

∠ABC=ACB

∠ADM=∠ABD+∠BAE+∠EAD

=∠ABD+∠BDC+∠CBE

=∠ABC+∠BDC

=∠ACB+∠BDC

=∠BDA+∠BDC

=∠ADC

CD=DM

△ADC?△ADM

AM=AC=AB

∠M=∠ABD=60

△ABM equilateral triangle

BM=AB

CD=AB-BD