How to answer the question, "where's yer brakes?"

find the racing line, brake before the apex, accelerate through.

Not really on topic, but there is nothing more satisfying while cycling than taking a corner at max speed, starting wide, clipping the apex and running right to the outside of the road/track/path, accidently did it one time me and a MTB riding friend (with much better brakes than me at this point) was on the inside and I wouldn't brake until he did, he eventually gave in, and I very very nearly went into the ditch on the outside, very scary, but oh so satisying.

There's a great cycling memory from me, now, as you were.