1.
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.
3
B.
6
C.
15
D.
21
Hint
2.
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 two points.
B.
Two distinct great circles intersect in exactly one point.
C.
Two distinct great circles intersect in exactly four points.
D.
Two distinct great circles intersect in infinitely many points.
Hint
3.
Which statement from Euclidean geometry is true in spherical geometry? Assume spherical points are restricted to be nonpolar points.
A.
A line has infinite length.
B.
Two perpendicular lines create four right angles.
C.
Two lines perpendicular to the same line are parallel to each other.
D.
Any two distinct points determine exactly one line.
Hint
4.
A line in plane Euclidean geometry is similar to a _____ in Spherical geometry.
A.
pole
B.
sphere
C.
great circle
D.
arc
Hint
5.
Perpendicular great circles form how many right angles?
A.
8
B.
4
C.
1
D.
2
Hint