From the chord theorem we know that:
[tex] \overline{TW}\cdot\overline{UW}=\overline{CW}\cdot\overline{VW} [/tex]
so:
[tex] \overline{TW}\cdot\overline{UW}=\overline{CW}\cdot\overline{VW}\\\\3\cdot\overline{UW}=x\cdot6\\\\3\cdot(\overline{TU}-\overline{TW})=x\cdot6\\\\
3\cdot(x+7-3)=x\cdot6\\\\3\cdot(x+4)=x\cdot6\\\\3x+12=6x\\\\12=6x-3x\\\\3x=12\qquad|\div3\\\\\boxed{x=4} [/tex]
Answer C.
