# I've Definitely Seen it Before

Geometry Level 4

In $$\Delta ABC$$ of area equal to $$1024$$ square units, points $$X$$, $$Z$$, and $$Y$$ divide the line segments $$\large \overline {BC}$$, $$\large \overline {CA}$$, and $$\large \overline {AB}$$ in the ratio $$\large 3:4$$, $$\large 5:6$$, and $$\large 1:2$$. The ratio of areas of $$\Delta XYZ$$ and $$\Delta ABC$$ can be expressed as $$\Large \frac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers.Determine the value of $$m+n$$.

Details- When I say $$X$$ divides $$\large \overline {BC}$$ in the ratio $$\large 3:4$$, I mean that $$\large \frac{BX}{XC}= \frac{3}{4}$$.

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