If you know BN and AN, then you can use the fact that ∆ AQB and ∆ ABN are similar. which gives the relation
BN/BQ = AN/AB = AB/AQ
Now
AN/AB = AB/AQ ⇒ AQ = AB²/AN = 36/AN
and
BN/BQ = AN/AB ⇒ BQ = (BN • AB)/AN = 6 • BN/AN
where AB = 6 because it's the diameter of the circle, and C(O, 3) means the circle has center O and radius 3.