Let AB and CD be chords of a circle, that meet at point Q inside the circle. If AQ = 6, BQ = 14, and CD = 38, then find the minimum length of CQ.
We have that
AQ * BQ = CQ * DQ
Let CQ = x and DQ = 38 - x
So
6 * 14 = x * (38 - x)
84 = 38x - x^2 reararrange as
x^2 - 38x + 84 = 0
Using the Quadratic Formula the minimum for x = CQ ≈ 2.3567
