In the given figure, the length of $B C$ is

(a) $7 c m$ (b) $10 c m$ (c) $14 c m$ (d) $15 c m$

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Solution

The correct option is (b): $10 c m$
Given: $B D = 3 c m, A F = 4 c m$ and $A C = 11 c m$
We know that the tangents drawn from an external point are equal.
$B F = B D = 3 c m$ (as they are tangents to the circle from external point B)
And, $A F = A E = 4 c m$ (tangents from external points A)
$A C = A E + E C$
$\Rightarrow 11 = 4 + E C$
$\Rightarrow E C = 7 c m$
Similarly, $E C = C D = 7 c m$ (tangents from external point C)
Now, $B C = B D + D C$
$B C = 7 c m + 3 c m$
$B C = 10 c m$

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