Let us consider an Regular n-sided Polygon of side length **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** .
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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.

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