8 particles are situated at corners of regular *octagon* of side **a**.
Each particle maintain a direction towards the particle at the next corner with a constant speed **v**, simultaneously a \(9^{th}\) particle(invisible to other 8 particles) starts at rest from the mid point of the side and move perpendicular to side with constant acceleration.

The acceleration of the \(9^{th}\) particle so that all the particles meet together at a point can be written as

\[\frac{a(\sqrt{b} - c)}{d}\]

Where 'b' is square free and \(\frac{a}{d}\) is in simplest form.

Then find

\(a + b + c + d\)

**Details and Assumptions**

Neglect any other collision

a = 7 (side length)

v = 4

All values are in SI unit

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