(4) Let $A$ and $B$ be the two endpoints of a diameter of a sphere, and $\pi$ be a plane passing through point $A$ and perpendicular to $AB$. $C$ and $D$ are two points on the sphere different from $A$ and $B$. Extend $BC$ and $BD$ to intersect the plane $\pi$ at points $E$ and $F$, respectively. If points $A$, $E$, and $F$ form an isosceles triangle, then the positional relationship between $AB$ and $CD$ is ( ).
(A) $AB$ is perpendicular to $CD$
(B) $AB$ is parallel to $CD$
(C) $AB$ is perpendicular and skew to $CD$
(D) Cannot be determined
(4) D Hint: If $A E=E F \neq A F$, then $A B$ and $C D$ are not perpendicular, eliminating options
$A$ and $C$; if $A B$ and $C D$ are parallel, then $A, E, F$ are collinear, and cannot form a triangle, eliminating
B. Therefore, the answer is D.