# 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 $$a+b+c+d$$.

×