If you learn to ski, once you get past the snowplow and some of the other basics, you eventually learn to PUT YOUR WEIGHT ON THE OUTSIDE SKI when you want to make a turn. I go down a tough run and I really STOMP on that outside ski. Corona Bowl at Stevens Pass. Some of the tougher stuff over on the left side coming down A Basin.
Riding a bike, I never really realized it isn't all that different. You want to make a really SHARP turn, PUT YOUR WEIGHT ON THE OUTSIDE PEDAL.
Try it. It works. You watch the video here, you'll notice most of the students wind up doing just that. I don't know if the instructors told them or they just sort of wound up doing it by trial and error.
I learned it in bicycle school. Thanks again, guys! Cycling is more like skiing than I thought...