Q. 15 5.0( 1 Vote )

In Fig. 10.80, the perimeter of ΔABC is


A. 30 cm

B. 60 cm

C. 45 cm

D. 15 cm

Answer :

Given:


AQ = 4 cm


BR = 6 cm


PC = 5 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.


By the above property,


AR = AQ = 4 cm (tangent from A)


BR = BP = 6 cm (tangent from B)


CP = CQ = 5 cm (tangent from C)


Now,


Perimeter of ∆ABC = AB + BC + CA


Perimeter of ABC = AR + RB + BP + PC + CQ + QA


[ AB = AR + RB


BC = BP + PC


CA = CQ + QA]


Perimeter of ABC = 4 cm + 6 cm + 6 cm + 5 cm + 5 cm + 4 cm


Perimeter of ABC = 30 cm


Hence, Perimeter of ∆ABC = 30 cm

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