第1题

The perpendicular bisectors 的 $A_iX$ 且 $A_{i+1}X$ 是also symmetry axes, so both pass through $O$. 因此 $OA_i=OX=OA_{i+1}$. But 每个点 strictly inside 三角形 $OA_iA_{i+1}$ lies strictly inside circum圆 through $O,A_i,A_{i+1}$ 译文：, whereas $X$ lies 上th在圆, a contradiction. 所以 $S$ has no extra 点s.