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