Question

In Fig. 10.78, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then,
A. AD = AB + BC + CA
B. 2AD = AB + BC + CA
C. 3AD = AB + BC + CA
D. 4AD = AB + BC + CA

Answer 1

this is your answer mujhe achcha laga ki main aapki madad ki

Answer 2

We know that tangents drawn from a point outside the circle are equal in length .

From the figure,

AD = AC + CD

⇒AD = AC + CF .....(1) Since ( CD = CF)

AE = AB + BE

⇒AE = AB + BF ......(2) Since ( BE = BF )

From equation (1) and (2)  we get

AD + AE = AC + CF + AB + BF

=> AD + AE = (AB + AC) + (BF + CF)

=> AD + AE = AB + AC + BC              {since BC = BF + CF}

=> AD + AD = AB + AC + BC              {since AE = AD}

=> 2AD = AB + BC + CA

Option b is correct.