(x-2)+(y-16)=169 what's the circles radius

The anwser is x=187-y

The graph can be divided into two shapes. A rectangle and a right triangle.

The distance that the rover will cover if it completes one circuit can be computed using the Pythagorean theorem and adding the sides of the rectangle.

Rectangle:
Width = 4 - 2 = 2 meters 
Length = 11 - 2 = 9 meters

Triangle = 16 - 2 = 14 ; 14 - 2 = 12 meters  (this is the short leg)
long leg of the triangle = length of the rectangle = 9 meters.

12² + 9² = c²
144 + 81 = c² 
225 = c² 
√225 = √c²
15 = c

Point A to B = 4 - 2 = 2 meters
Point B to C = 15 meters
Point C to D = 16 - 2 = 14 meters
Point D to A = 11 - 2 = 9 meters

Total distance traveled = 2 + 15 + 14 + 9 = 40 meters.