63 Take a point $X$ inside or on the circumference of a circle. Draw two perpendicular chords $A C$ and $B D$ through point $X$ (when $X$ is on the circumference, a degenerate case is allowed, i.e., one chord is a diameter and the other chord shrinks to a point). For all possible choices of $X$, find the maximum and minimum values of $S=|A C|+|B D|$.
63 As shown in Figure 28, it is clear that \( AC + BD \leq 2d \), where \( d \) is the diameter of the circle. The maximum value is achieved when \( X \) coincides with the center \( O \) of the circle.
Furthermore, draw a line through \( B \) parallel to \( AC \) intersecting the circle at \( E \), then \(\overparen{BE} \leq \overparen{AC}\) so \( BE \leq AC \)
\[
BD + AC \geq BD + BE \geq ED = d
\]

When \( X \) is on the circumference of the circle, the minimum value \( d \) can be achieved.