1. Let \(\overline{AB}\) and \(\overline {CD}\) be chords of a circle, that meet at point Q inside the circle. If AQ = 6, BQ = 12, and CD = 38, then find the minimum length of CQ.
2. Let \(\overline{XY}\) be a tangent to a circle, and let \(\overline{XBA}\) be a secant of the circle, as shown below. If AX = 15 and XY = 9, then what is AB?
I have found an answer wich was 27/5 but that was incorrect.
3. Let \(\overline{TU}\) and \(\overline{VW}\) be chords of a circle, which intersect at S, as shown. If ST = 3, TU = 15, and VW = 3, then find SW.
I have also found the answer 6 but it was also incorrect.
Thank you in advance
