# Integer Lengths

Geometry Level 4

Given triangle $$ABC$$, let $$P$$ be a point on $$AB$$ and $$Q$$ be a point on $$AC$$.

$$PQ \cap BC=X$$ and $$\angle PXB=\angle C - \angle B$$

$$PC \times QB=1000$$ and $$PB \times QC=371$$.

Given that $$BC>PQ>1$$ and $$BC$$ and $$PQ$$ are integers, find the length of $$BC$$.

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