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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

 Jun 27, 2020
 #1
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1. By power of a point, CQ = 14.

 

2. By power of a point, AB = 8.

 

3. By power of a point, ST*TU = SV*VW ==> 3*15 = SV*3  ==> SV = 15, so SW = 18.

 Jun 27, 2020
 #2
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I am sorry it was incorect..

Guest Jun 28, 2020

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