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Parting 4 ways

Geometry Level 3

The following figure is a triangle $ABC$ , where $AB=5, BE = y, EC=4, CF = x, AF = 6-x$ .

The point $D$ is the Incenter of this triangle. Find the value of $x+y$ .

\frac{199}{30}

\frac{13}{2}

\frac{766}{111}

4

\frac{511}{3}

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by Victor Paes Plinio

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