# Circle and triangle

Geometry Level 5

Above shows a triangle $$XYZ$$ with $$XY= 18, YZ=16, XZ=14$$. The bisector of angle $$X$$ meets the straight line $$YZ$$ at point $$W$$.

The circle passing through point $$X$$ and touching $$YZ$$ at $$W$$ cuts $$XY$$ and $$XZ$$ at points $$M$$ and $$N$$ respectively.

Find the distance $$MN$$.

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