In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then Options: A . &nbsp A D = A B + B C + C A B . &nbsp 2 A D = A B + B C + C A C . &nbsp 3 A D = A B + B C + C A D . &nbsp 4 A D = A B + B C + C A

In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and

Question

In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then

Options:

A .

A D = A B + B C + C A

B .

2 A D = A B + B C + C A

C .

3 A D = A B + B C + C A

D .

4 A D = A B + B C + C A

Answer: Option B
:
B

We know that

$A D = A E$

$A D = A B + B E$

Since $B E = B F$ as tangents drawn from an external point to a circle are equal , $A D = A B + B F$ ……(1)

Also

$A D = A C + C D$

$A D = A C + C F$ ……(2) ( $C D$ and $C F$ are tangents drawn from the external point C to the circle)

Adding equation (1) and (2),

$A D + A D = A B + B F + C F + A C$

$2 A D = A B + B C + A C$

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