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?