Geometric Construction 11
1.Illustrate Pascal's Mystic Hexagram Theorem for a Circle: The points
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
5.Illustrate Brianchon's Theorem for a Circle: If a hexagon is circumscribed
construct the conic passing through the three points
and tangent to the lines
at the given points.
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
points on two of them.