1. Which statement does NOT hold true in spherical geometry? A. An arc of a great circle is the shortest path between two points. B. There is a unique great circle passing through any pair of nonpolar points. C. A great circle is finite and returns to its original starting point. D. If three points are collinear, exactly one is between the other two. Hint 2. Points M, N, and P lie on a great circle as shown. If MN = 9 and NP = 12, what is the distance between M and P through N? A. 21 B. 15 C. 6 D. 3 Hint 3. A property from plane Euclidean geometry is written below. Which of the following is a corresponding statement for non-Euclidean spherical geometry?Two distinct intersecting lines intersect in exactly one point. A. Two distinct great circles intersect in exactly one point. B. Two distinct great circles intersect in exactly two points. C. Two distinct great circles intersect in infinitely many points. D. Two distinct great circles intersect in exactly four points. Hint 4. Which statement from Euclidean geometry is true in spherical geometry? Assume spherical points are restricted to be nonpolar points. A. Any two distinct points determine exactly one line. B. Two lines perpendicular to the same line are parallel to each other. C. A line has infinite length. D. Two perpendicular lines create four right angles. Hint 5. Which statement is not true? A. M, N, and P all lie on the same great circle. B. M is between N and P C. N is between P and M D. P is not between M and N. Hint