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.