To find the length of C'B', we can use the distance formula. Let's calculate it step by step.
First, let's find the coordinates of C' and B' after the dilation. Since the circle is dilated by a scale factor of 3 about the origin, we can multiply the x and y coordinates of C and B by 3.
C' = (3 * 8, 3 * 10) = (24, 30)
B' = (3 * 12, 3 * 13) = (36, 39)
Now, let's use the distance formula to find the length of C'B':
d = √((x2 - x1)² + (y2 - y1)²)
d = √((36 - 24)² + (39 - 30)²)
d = √(12² + 9²)
d = √(144 + 81)
d = √225
d = 15 units
Therefore, the length of C'B' is 15 units.