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- Line through 2 points. Construct the line AB through two points
A and B.
- Perpendicular line. Given a point C not on line AB, construct
the line through C orthogonal to line AB.
- Asymptotic parallels. Given an ideal point X and a point E,
construct the line through E and X. Given a point C not on line AB,
construct the two lines through C which are asymptotically parallel
to line AB.
- Ultraparallels. Given two ultraparallel lines m = line AB and
n = line CD, construct the line p that is orthogonal to both.
- Line Reflection. Given a point C, construct the reflection
C' of C in line AB.
- Perpendicular Bisector as Mirror Line. Given points A and B,
construct the line m which reflects A to B. Be sure to include the case
when B is the center of the P-disk. (This line will be the perpendicular
bisector when distance is defined. Notice that this means than any point
can be moved to any other by a line reflection.)
- Circle given center and radius. Given a point A and a point
B, construct the circle with center A through B. (Hint: This circle
is a P-circle. As will be explained by an experiment below, a P-circle
is actually a Euclidean circle in the interior of the disk of the P-model.
As in the DWEG model and the Stereo model, the P-center is not the Euclidean
center, for a P-diameter of the circle is a P-line orthogonal to the
circle.0
- Circle given diameter. Given points A and B, construct the
circle with diameter AB
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