In the adjoining figure, if AD, AE, and BC are tangents to the circle at D, E, and F respectively, which of the following is true?

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

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

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

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

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Solution

The correct option is B
$2 A D = A B + B C + C A$

We know that

$A D = A E$

$A D = A B + B E$

$B E = B F$ are tangents drawn from the external point B to a circle, so $B E = B F$ .
$A D = A B + B F$ … (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 equations (1) and (2),

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

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

Suggest Corrections

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