1), it is proved that if AC and EF intersect at H point, because E point and F point are the midpoint of edges CD and CB respectively, according to triangle reasoning, H point is the midpoint of line segment Co. Because of the law of prism bisector, O is the midpoint of DB, then H is also the midpoint of EF, and AH is perpendicular to EF. Because the triangle AFE is an equilateral triangle, AH is the perpendicular bisector of the EAF angle. And because the line segment AO= the line segment CO=2 times OH, so the O point is the intersection of the perpendicular lines of the three angles of the equilateral triangle EFA. Then point o is the center of the circumscribed circle passing through points e, f and a, so it is proved that. Actually, it's nothing. It's just a little troublesome to write. If I get extra points, I will consider answering them all at once.