Let AB and 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.
AQ * BQ = CQ * DQ
6 * 12 = x * (38 - x)
72 = 38x - x^2 rearrange as
x^2 - 38x + 72 = 0 factor
(x - 36) ( x - 2) = 0
The second factor set to 0 and solved for x gives the minimum length of CQ
x - 2 = 0
x = 2 = CQ
