1)

Connect AC, CE, AD

According to the vertical diameter theorem, arc AC = arc AD = arc CE.

So ∠ CAE = ∠ CEA = ∠ ACD = ∠ ADC

So △ ace△ ACD

So CD = AE = 8

So oc = CD/2 = 4

So the coordinate of point C is C (0 0,4).

2)

Connecting CM

From 1), we know that ∠CEA=∠ACD.

So ag = CG

So g is on the vertical line of AC.

Because cm = am

So m is on the vertical line of AC.

So the straight line MG is the middle vertical line of AC.

So MG⊥AC

Because AB is the diameter

So AC⊥BC

So MG‖BC

For reference! JSWYC