# A Partitioned Equilateral Triangle

Geometry Level 3

Above shows an equilateral triangle $$ABC$$ with side length 1. Given that $$M, N$$ and $$Q$$ are points on the sides $$AB, BC$$ and $$AC$$ such that the lines $$AN, BQ$$ and $$CM$$ divide the triangle into 4 triangles and 3 quadrilaterals.

We color the triangles in two colors (orange and green) in such way that any two triangle with a common vertex are colored with different colors.

If the area colored in green is equal to that colored in orange, find the value of $$AM+BN+CQ$$.

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