Sendov's reformulated conjecture for an interior zero

Let

$$P(z)=(z-a)\prod_{j=1}^{n-1}(z-z_j),$$

with $a\in(0,1)$ and $|z_j|\leq 1$ for $j=1,\ldots,n-1$. Sendov's reformulated conjecture. The disk

$$|z-a|\leq 1$$

contains a critical point of $P(z)$. This is a reformulation obtained using known special cases at a zero on the unit circle and at the zero $0$, together with rotational invariance; the general conjecture remains open.