In Q. No. 1, if PB = 10 cm, what is the perimeter of Δ PCD?

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


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