Draw $n$ random chords in a circle. What is the expected number of sides of the polygon that contains the center, as $n\to\infty$?

Draw $n$ random chords in a circle. Each chord connects two independent uniformly random points on the circle.

Here is an example with $n=40$.

In this example, the centre of the circle (shown in red) is contained by a pentagon.

Let $f(n)=$ expected number of sides of the polygon that contains the centre of the circle.

What is $\lim\limits_{n\to\infty}f(n)$?

I used a random chord generator to run $50$ trials each with $n=10,15,25,40$ and got the following results.

This is a follow-up question to the question"Draw $n$ random chords in a circle. What is the distribution of the kinds of polygons, as $n\to\infty$?"

Edit: Ignore cases in which the centre of the circle is not contained by a polygon, i.e. is contained by a region with a curved edge.