Question

I would like to know what is the value of z

Answer 1

From the chord theorem we know that:

$\overline{TW}\cdot\overline{UW}=\overline{CW}\cdot\overline{VW}$

so:

$\overline{TW}\cdot\overline{UW}=\overline{CW}\cdot\overline{VW}\\\\3\cdot\overline{UW}=x\cdot6\\\\3\cdot(\overline{TU}-\overline{TW})=x\cdot6\\\\ 3\cdot(x+7-3)=x\cdot6\\\\3\cdot(x+4)=x\cdot6\\\\3x+12=6x\\\\12=6x-3x\\\\3x=12\qquad|\div3\\\\\boxed{x=4}$

Answer C.