14.5 (IMO 26 Pre) Given a circle and a line $l$ in the same plane, the center of the circle is at point $O$, the radius is $r$, and the distance from $O$ to $l$ is $d$, with $d > r$. Choose two points $M$ and $N$ on $l$ such that the circle with $MN$ as its diameter is externally tangent to the given circle. Find a point $A$ in the plane such that for all $M, N, \angle MAN$ is a fixed angle.
14. 5 Let $l$ be the $x$-axis, and the $y$-axis is a line through the center $O$ of a given circle, perpendicular to the $x$-axis. For a circle that is externally tangent to the given circle, with its center at $(h, 0)$ and radius $s$, it must satisfy $h^{2}+d^{2}=(r+s)^{2}$. The coordinates of points M and N are $(h-s, 0)$ and $(h+s, 0)$, respectively. By symmetry, the point $A$ that satisfies the condition must lie on the $y$-axis, set $A(0, k)$, here, we can assume $k>0$. We can obtain $\tan \angle M A N=\frac{2 s k}{h^{2}-s^{2}+k^{2}}=\frac{2 s k}{2 s r+r^{2}+k^{2}-d^{2}}$. Therefore, the value is a constant independent of $s$ if and only if $k^{2}=d^{2}-r^{2}$.