Question

In Fig. the perimeter of ΔABC is

A. 30 cm 

B. 60 cm 

C. 45 cm 

D. 15 cm

Answer 1

Answer is A. 30 cm

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