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In Fig, PA and PB are tangents to the circle drawn from an external point P. CD are a third tangent touching the circle at Q. If PB = 10 cm, what is the perimeter of Δ PCD?

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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) 


CA = CQ= 10 cm (tangent from C) 


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

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