# Right Triangles In Regularity (Advanced 1)

Geometry Level 4

As shown in the figure, $$K$$ is the midpoint of one side $$AC$$ of the equilateral triangle $$\Delta{ABC}$$, which has a RIGHT angle $$\angle{MKN}$$ inside with two intersections $$M$$ and $$N$$ with $$AB$$ and $$BC$$, respectively.

Given $$AM=6$$ and $$CN=\frac{4}{5}$$, so that $$MN$$ can be found in length as $$\dfrac{b}{a}\sqrt{c}$$ with $$a$$ and $$b$$ coprime positive integers and $$c$$ square-free. Also we can find $$AC$$ in length as a positive integer $$d$$.

Find $$a+b+c+d$$.

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