Given:
PB = 10 cm
CQ = 2 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,
PA = PB = 10 cm (tangent from P)
DB = DQ= 10 cm (tangent from D)
And,
CA = CQ= 10 cm (tangent from C)
Now,
Perimeter of ∆PCD = PC + CD + DP
= PC + CQ + QD + DP
= PC + CA + DB + PD [∵CA = CQ and DB = DQ]
= PA + PB [∵PA = PC + CA and PB = PD + BD]
= 10 cm + 10 cm
= 20 cm
Hence, Perimeter of ∆PCD = 20 cm