Theorem: If two chords intersect within a circle, then the product of the lengths of the segments (parts) of one chord is equal to the product of the lengths of the segments of the other chord.
In your case this theorem sounds as
[tex]2\cdot x=3\cdot 6.[/tex]
Solve this equation:
[tex]x=\dfrac{3\cdot 6}{2}=9.[/tex]
Answer: correct choice is C.
