In Kansas, pedestrians have the right-of-way within crosswalks at all intersections, including roundabouts. However, pedestrians must not suddenly leave a curb or other safe waiting place and walk into the path of a vehicle if it is so close that it is an immediate hazard.

Do not cross the roundabout to the central island or walk in the driving lanes.

Use the crosswalks on the legs of the roundabout.
If there is no crosswalk marked on a leg of the roundabout, cross the leg about one vehicle-length away from the circular roadway of the roundabout.

Look and listen for approaching traffic.
Choose a safe time to cross from the curb to the median opening.  Although you have the right-of-way, if approaching vehicles are present, be sure drivers recognize you’re there and intend to cross.  When crossing an entry or exit with more than one lane, be sure that oncoming vehicles in all lanes and directions come to a complete stop before proceeding.

Use the splitter island.
It allows you to cross one direction of traffic at a time.

typical collision

Visually impaired individual prepares to cross in a rural area