Hardcore Analytic Geometry

As shown above, the ellipse has equation: $\dfrac{x^2}{24}+\dfrac{y^2}{5}=1$ , and point $P$ has coordinate $(2,1)$ . Line $l_1$ has positive slope and passes through $P$ and it intersects with the ellipse at point $A,B$ .

$C,D$ are two other points on the ellipse such that the angle bisectors of $\angle ACB$ and $\angle ADB$ both pass through $P$ .

Let $E$ be the circumcircle of $\triangle PCD$ . Find the minimum radius of circle $E$ .

If the minimum radius is $R$ , submit $\lfloor 10000R \rfloor$ .

Inspiration: Circles of Apollonius of a Triangle