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.
AQ * BQ = CQ * DQ
16 * 12 = 192
16 * 12 = CQ(36 - CQ)
CQ = 2(9 - √33) (CQ ≈ 6.51)
DQ = 2(9 + √33) (DQ ≈ 29.49)
