Centre of LOVE 2

Geometry Level 3

A quadrilateral \(LOVE\) has the coordinates of the vertices as \(L=(2,5)\), \(O=(6,\frac{71}{12})\), \(V=(5,1)\) and \(E=(0,\frac{17}{12})\). Find the coordinates of the meeting point of its diagonals.

If the required coordinates can be written as \((\frac{a}{b},\frac{c}{d})\), where \(\gcd(a,b)=1\) and \(\gcd(c,d)=1\), find the value of \(a+b+c+d\).

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