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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