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Find AB?

Question

Find AB?

A

7

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B

6

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C

8

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D

None of these

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Solution

The correct option is B 6

$A C \times A D = A F \times A E$ [Secant Theorem]
$4 \times 9 = 3 \times (3 + x)$
$(s a y, E F = x) \Rightarrow x = 9$
Now apply tangent secant theorem in 2nd circle
$A B^{2} = A F \times A E$
$A B^{2} = 3 \times 12$
$A B = 6$
Hence, b is the correct option.

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