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Let line AB and line CD be chords of a circle, that meet at the point Q inside the circle. If AQ = 16, BQ = 12, and CD = 36, then find the minimum length of CQ. 

 Apr 17, 2021
 #1
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AQ * BQ = CQ * DQ

16 * 12 = 192

16 * 12 = CQ(36 - CQ)

CQ = 2(9 - √33)         (CQ ≈ 6.51)

 Apr 18, 2021
 #2
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DQ = 2(9 + √33)         (DQ ≈ 29.49) smiley

Guest Apr 18, 2021

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