Can I just clear up a point? @G2EWS has confused two principles, which is the fastest safe speed to take any given corner, but that is based on that corner having full sight lines, therefore the "racing line" (out,apex,out) simply extends the geometry of the curve and means a car can travel round that curve "safely", ie without losing grip.
However, the police driving manual also talks of sight lines, and the "arrowhead" effect, which is the point at which the sides of the road appear to converge. Too fast, and that point rushes towards you, bang on the right speed and the arrowhead stays at a constant distance until the road straightens again. That arrowhead principle also teaches a driver to shift position in the road to extend that arrowhead, for example by moving to the offside edge of the carriageway to extend the sight lines on a left hander, and as far over to the nearside as possible on a right hander.
Absolutely none of this theory over rides the most fundamental principle of safe cornering, which is that YOU MUST AT ALL TIMES BE TRAVELLING AT SUCH AS SPEED THAT YOU CAN STOP SAFELY WITHIN THE DISTANCE YOU CAN SEE AHEAD. Oh, and the other point made above, which is that the vehicle should be able to stay on the correct side of the road.
So sorry G2EWS, but if you had to make an emergency stop to avoid the cyclist, you were simply travelling too fast. Please don't fall out with me, I'm not doing this as a personal attack, but a little knowledge is a dangerous thing. Unless you have done all of the Advanced driving course, leave fast cornering to the experts, or the race track.