‘A’ and ‘B’ are two fixed points in a field. A cyclist C moves such that ACB is always a right angle. In this context, which one of the following statements is correct?

By Thales' theorem, for fixed points A and B the locus of points C for which ∠ACB = 90° is the circle having AB as diameter; every point on that circle subtends a right angle at C. Thus a cyclist constrained so that ACB is always a right angle will move along the circle with AB as its diameter. This motion is therefore possible (except at the degenerate positions where C coincides with A or B) and is not an ellipse or an exponential curve. Standard circle-geometry results about diameters and right angles corroborate this conclusion [1]. Hence option 2 (circle) is correct.

Sources

1. [1] https://amsi.org.au/teacher_modules/Circle_Geometry.html