X =

A. 3

B. 7

C. 1

(Special Segments)

Option A:

x = 3

Solution:

Special segments in a circle:

If two secant segments are drawn to a circle from a exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

⇒ 9 × 4 = x × 12

⇒ 36 = 12x

Divide by 12 on both sides, we get

⇒ 3 = x

Switch the sides of the equation.

⇒ x = 3

The value of x is 3.

Hence option A is the correct answer.

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