Answer
We must prove that triangle TWV is similar to triangle TXV. Both triangles share a common angle T and a common side TV, which are congruent to themselves by the identity property. In addition, angles V and W are congruent, for they are inscribed angles for the same arc. Thus, the triangles are similar by ASA, so we use proportions:
$\frac{TV}{TW}=\frac{TX}{TV} \\TV^2 =TWTX$