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

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SUMMARY

The discussion focuses on proving that the center of segment DG is equivalent to the center of the red circle formed by the intersection of extended lines from squares BCED and ACFG. Key steps include extending line FC to intersect point D, extending line EC to intersect point G, and demonstrating that the intersection of lines GA and DB at point X lies on the red circle, with CX serving as its diameter. Additionally, it is established that quadrilateral CDXG is a parallelogram, confirming that its diagonals intersect at the circle's center.

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

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I don't know how to start
 

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maxkor said:
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.
 

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