In the adjoining figure, if AD, AE and BC are tangents to the circle at D, E and F respectively. Then Options: A . &nbspAD=AB+BC+CA B . &nbsp2AD=AB+BC+CA C . &nbsp3AD=AB+BC+CA D . &nbsp4AD=AB+BC+CA

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 . AD=AB+BC+CA

B . 2AD=AB+BC+CA

C . 3AD=AB+BC+CA

D . 4AD=AB+BC+CA

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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