[Alan Anderson]

Simple and obvious answer: the turning radius is the distance between the robot and the center of the circle it travels while turning.

Simple observation: the wheels are moving along the circle, in a direction perpendicular to the direction to the center of the circle.

Insightful comment: The axle of each wheel is perpendicular to its direction of travel, and thus points to the center of the circle. All you need to do is find the point of intersection of the lines extending from the front and rear axles. The distance from that point to the robot is the turning radius.