# Distance Between Intersection Points

Geometry Level 4

On a semicircle with diameter $$AB$$ and centre $$O$$ points $$X$$ and $$Y$$ are chosen such that $$\angle XOY = 120^{\circ}$$. Let $$AX$$ and $$BY$$ meet at $$Z$$ and $$AY$$ and $$BX$$ meet at $$W$$. If $$AB = 5\sqrt{3}$$, find $$WZ$$.

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