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.
+129847 Intersecting Chord Theorem
AQ * BQ = CQ * DQ
16 * 12 = CQ ( 36 - CQ)
192 = 36CQ - CQ^2 rearrange as
CQ^2 - 36CQ + 192 = 0 complete the square on CQ
CQ^2 - 36CQ = -192
CQ^2 - 36CQ + 324 = -192 + 324
(CQ - 18)^2 = 132 take the negative root
CQ - 18 = -sqrt (132)
CQ - 18 = -2sqrt 33
CQ = 18 - 2sqrt (33) ≈ 6.51 = min length of CQ
EDIT TO CORRECT A PREVIOUS ERROR !!!!!
+1694 Check your answer again. Why didn't you use the quadratic formula to solve this problem?!?
36 - 4.144 = 31.856
4.144 * 31.856 = 132.011264
+1694 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.
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I didn't see the word integer
AQ * BQ = CQ * DQ
16 * 12 = CQ(36 - CQ)
CQ = 2(9 - √33)
