**d** , Initially **n** identical particles each of mass **m** are placed rest at the vertices of the polygon. Then at time **t=0** they start moving with constant speed ${ v }_{ o }$ each such that they always moves in direction towards the adjacent particle. Let the total time taken by particles when they meets is **T** .

If circum-radius of the Regular polygon is **R** and it's in-radius is **r** .

If the value of

$\frac { r }{ R } \quad =\quad \sqrt { 1-\quad (\cfrac { x }{ y } \times \frac { d }{ { v }_{ o }T } ) }$.

Then Find value of $1729\quad \times \quad \cfrac { x }{ y } \quad$

**Details and assumptions**

$\bullet$ **x** and **y** are positive co-prime integers.