Apollonius-boundary conjecture for active pursuers in the MPSE problem

Let an MPSE problem have pursuers and evaders at positions at time $t$, with $0\leq t<t_c$. Let $\mathcal{B}^t$ be the Apollonius boundary and let $\mathcal{A}_i$ denote the Apollonius circle associated with pursuer $P_i$. Assume that the pursuers follow a constant bearing strategy. Apollonius-boundary conjecture. Pursuer $P_i$ is active at time $t$ if

$$\mathcal{B}^t\cap\mathcal{A}_i\neq\varnothing,$$

and is redundant otherwise. The conjecture provides the criterion used by the proposed algorithm to identify active and redundant pursuers in a multiple-pursuer, single-evader problem; the supplied text gives no evidence that it has been proved or disproved.