Amy and fraser walk inside a circular lawn. point b is the center of the lawn, as shown below: a circle is drawn. the center of the circle is labeled b. points a and c are on the circumference of the circle. a straight line passes though b and joins points a and c. amy walks from point a to point b along the segment ab. fraser walks from point a to point c along the segment ac. which statement is correct?

The complete question is
Amy and Fraser walk inside a circular lawn. Point B is the center of the lawn, as shown below: A circle is drawn. The center of the circle is labeled B. Points A and C are on the circumference of the circle. A straight line passes though B and joins points A and C. Amy walks from point A to point B along the segment AB. Fraser walks from point A to point C along the segment AC. Which statement is correct?

A) Both Amy and Fraser walk distances equal to the diameter of the lawn.

B) Amy walks a distance equal to the radius, and Fraser walks a distance equal to the diameter of the lawn.

C) Both Amy and Fraser walk distances equal to the radius of the lawn.

D) Amy walks a distance equal to the diameter, and Fraser walks a distance equal to the radius of the lawn.

the picture in the attached figure

we know that
if a straight line passes though B and joins points A and C
then
AC is the diameter of the circle
and
AB=BC------> is the radius of the circle
so

Amy walks from point A to point B along the segment AB
that means that Amy walks the radius

Fraser walks from point A to point C along the segment AC
that means that Fraser walks the diameter

therefore

the answer is
the option
B) Amy walks a distance equal to the radius, and Fraser walks a distance equal to the diameter of the lawn.