The vertices of the square $ABCD$ are the centers of four circles, all of which pass through the center of the square. Prove that the intersections of the circles on the square $ABCD$ sides are vertices of a regular octagon.
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Tags: geometry, Regular, octagon, square
The vertices of the square $ABCD$ are the centers of four circles, all of which pass through the center of the square. Prove that the intersections of the circles on the square $ABCD$ sides are vertices of a regular octagon.