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svetoff [14.1K]
3 years ago
9

Find the value of X

Mathematics
1 answer:
aivan3 [116]3 years ago
6 0

The value of x is 9.

Solution:

AB is a tangent and BD is the secant.

AB = 12, BC = 9 and CD = x

BD = BC + CD

BD = 9 + x

<em>The product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.</em>

AB^2=BC\times BD

12^2=9\times (9+x)

144=81+9x

Subtract 81 from both sides.

144-81=81+9x-81

63=9x

Divide by 9 on both sides.

$\frac{63}{9} =\frac{9x}{9}

9=x

The value of x is 9.

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