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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.

Jun 27, 2020

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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