In the figure, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA=4cm, BP=3cm and AC=11cm, then the length of BC (in cm) is:

As given PA=4cm BP=3cm ∴ AB=4+3=7cm AC=11cm As PA and RA is two tangents from same external point A ∴ RA=PA=4cm ⇒ RC=AC−RA ⇒ RC=11−4=7cm As RC and QC is two tangents from same external point C ∴ QC=RC=7cm As BP and BQ is two tangents from same external point B ∴ BP=BQ=3cm Then BC=QC+BQ ⇒ BC=7+3=10cm