The Predator and the Prey solution

[P6 - S2 Maths: Circles] Hey, hope you enjoyed the two-week suspense. Please don't agonise over it like my kids did.

Kept you waiting, huh? Haha. Here's the solution as promised:

Wow, that's a mouthful! Thankfully, Professor Ben Sparks has a much more geometric (and intuitive) explanation, right here:

Isn't it wonderful how the event horizons intersect and allow the duck / mouse to escape?

For those interested in higher level mathematics, the predator will always win if their speed is at least (𝜋 + r) time faster than the mouse. Bonus question: Prove that the prey can no longer escape when the predator's speed is equal to (𝜋 + r). You may opt for a visual proof, a direct proof or a proof by contradiction.