Given:

AR = 4 cm

BR = 3 cm

AC = 11 cm

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.

Using the above property,

AR = AQ = 4 cm (tangent from A)

BR= BP (tangent from B)

And,

CP = CQ (tangent from C)

Also,

CQ = CA – AQ = 11 cm – 4 cm = 7 cm

Now,

BC = BP + PC

= BR + CQ [∵ BR = BP and CP = CQ = 7 cm]

= 3 cm + 7 cm

= 10 cm

Hence, BC = 10 cm