MHB Prove that center of DG = center of the red circle.

[maxkor]

Let BCED and ACFG square. Prove that center of DG = center of the red circle.

View attachment 6025

I don't know how to start

 

[Opalg]

Let BCED and ACFG square. Prove that center of DG = center of the red circle.
I don't know how to start

Extend some of the lines in the figure.

• Show that if you extend the line FC then it passes through D.

• Show that if you extend the line EC then it passes through G.

• Show that if you extend the lines GA and DB to meet at X then X lies on the red circle, and CX is a diameter of the circle.

• Show that CDXG is a parallelogram whose diagonals meet at the centre of the circle.