The proof of the three reflections theorem begins, as it did for R², by considering the equidistant set of two points. 7.4.1 Show that the equidistant set of two points in R³ is a plane. Show also that the plane passes through O if the two points are both at distance I from O. 7.4.2 Deduce from Exercise 7.4.1 that the equidistant set of two points on $² is a "line" (great circle) on S². Next, we establish that there is a unique point on $2 at given distances from three points not in a "line." 7.4.3 Suppose that two points P.Q= $2 have the same distances from three points A,B,C S² not in a "line." Deduce from Exercise 7.4.2 that P=Q. 7.4.4 Deduce from Exercise 7.4.3 that an isometry of $2 is determined by the images of three points A, B,C not in a "line."