Distance Between Intersection Points

Geometry Level 4

On a semicircle with diameter ABAB and centre OO points XX and YY are chosen such that XOY=120\angle XOY = 120^{\circ}. Let AXAX and BYBY meet at ZZ and AYAY and BXBX meet at WW. If AB=53AB = 5\sqrt{3}, find WZWZ.

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