Problem 1.89

A cyclist rides along the circumference of a circular horizontal plane of radius \(R,\) the friction coefficient being dependent only on distance \(r\) from the centre \(O\) of the plane as \(k=k_{0}(1-r / R),\) where \(k_{0}\) is a constant. Find the radius of the circle with the centre at the point along which the cyclist can ride with the maximum velocity. What is this velocity?