<ABM = (1/2) * arc AM and <CBM = (1/2) * arc DM

Inscribed angle measures half its intercepted arc

<CMB = 90

Substitution

Inscribed angle measures half its intercepted arc

The angles in a linear pair are supplementary

Substitution

<ABM = <CBM

Reflexive

Triangle AMB is congruent to Triangle CMB

Circle O with diameter AB, arc AM = arc DM

<AMB = 90

arc AB = 180

ASA (Angle-Side-Angle)

Given

MB = MB

<AMB = (1/2) * arc AB

Definition