AB is a diameter, therefore angle BCA=90 degrees.

Therefore angle CAO is 90-37=53 degrees.

Triangle AOC is isosceles as two sides are radius length.

Therefore angle CAO=angle OCA.

Also side AC is perpendicular to side OM.

Angle CBA=37 degrees, so angle MAO is 90-37=53 degrees.

Therefore angle MCO=53 degrees, angle MOC=37 degrees.

Or angle BCA is 90 degrees.

Angle OMA is 90 degrees, therefore line OM is parallel to side BC.

Hence angle OMA=angle BAC.

Triangle OCA is isosceles and is split into 2 identical right angled triangles.

Therefore angle MOA=angle MOC.