Given: ∠PBR = ∠QBR & PQ ∥ AC.
BR bisects ∠B such that ∠PBR = ∠QBR.
Since angle-bisector theorem says that, if two angles are bisected in a triangle then it equates their relative lengths to the relative lengths of the other two sides of the triangles.
So by applying angle-bisector theorem, we get
⇒ QR × BP = PR × BQ
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