Geometric Construction 11
1.Illustrate Pascal's Mystic Hexagram Theorem for a Circle: The points
12,
23, 31 of the intersection of the three pairs of
opposite sides 1'2 and 12', 2'3
and 23', 3'1 and 13' of a hexagon 12'31'23' inscribed
in a circle lie on a line.
2.Construct the conic passing through five given points.
3.Construct the conic passing through four given points and tangent
to a given
line which contains one of the points.
4.Given three points and two lines each containing one of the
points,
construct the conic passing through the three points
and tangent to the lines
at the given points.
5.Illustrate Brianchon's Theorem for a Circle: If a hexagon is circumscribed
about a circle, the three joining pairs of opposite
vertices are concurrent.
6.Construct the conic tangent to five given lines.
7.Construct the conic tangent to four given lines and passes through
a point on
one of them.
8.Construct the conic tangent to three given lines and passes through
two
points on two of them.
