Given:

PA = 4 cm

BP = 3 cm

AC = 11cm

Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.

By above property,

AP = AR = 4 cm (tangent from A)

BP = BQ = 3 cm (tangent from B)

QC = RC (tangent from C)

Clearly,

RC = AC – AR

⇒ RC = 11 cm – 4 cm

⇒ RC = 7 cm

Now,

BC = BQ + QC

⇒ BC = BQ + RC [∵ QC = RC]

⇒ BC = 3 cm + 7 cm

⇒ BC = 10 cm

Hence, BC = 10 cm