Cycler on a winding and velocity

[Glyper]

Homework Statement

A cycler is going through the winding, cycling on a circle of radius 6m and is slanting with alpha=75^ to the horizontal surface. What's his velocity?

Homework Equations

T=\frac{mv^{2}}{R}
Fc=\mu F_{N}

The Attempt at a Solution

We have two forces on the cycler - centrifugal force and friction. They are equal (or at least should be? Though I don't know why...) so we have T=Fc and thus \frac{mv^{2}}{R}=\mu F_{N}. How should I use it, though, if I have only 75^ and the radius given?

 

[Spinnor]

Does this look right?