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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