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