The dynamic geometry of Apollonius circle

In this paper, I present a new application of the Apollonius circle in a game design context. Instead of determining the meeting point from the initial conditions, in the present proposal a previously prescribed interception point is given and I calculate the instant of time that the torpedo must be launched. In the problem proposed in reference [¹] the torpedo and the ship start at the same time (on a straight path) towards the point of interception. Now I pose the following question: What happens if we wait a certain time $t$ to launch the torpedo? What happens if we aim the torpedo to a certain point and we want to know the instant the ship is hit when passing through this point? These are the new questions addressed to in this note.

Keywords:
pursuit problems; computational simulation; educational software