This doesn't look like a special Trapezoid!!!!

Geometry Level pending

A trapezoid \(ABCD\) has \(AB||CD\). The lengths of segments \(AB\), \(BC\), \(CD\) and \(AD\) are \(7,8,9\) and\(10\). The external bisectors of \(\angle A\) and \(\angle D\) meet at \(P\), and the external bisectors of \(\angle B\) and \(\angle C\) meet at \(Q\). Find the length of \(PQ\).

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