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Geometric Construction 9

Construct an animation displaying two cardioids having the same cusp and
are orthogonal to each other.

Illustrate Pascal's Theorem for the circle: If a hexagon is inscribed in
a circle, the three pairs of opposite sides meet in collinear points.

Construct a conic passing through five given points.

Construct the conic given a tangents and the point of contact and passing
through three other given points.

Construct the conic given two tangents and the points of contact and passing
through one other given point.

Illustrate Brianchon's Theorem for circle: If a hexagon is circumscribed
about a circle, the three diagonals are concurrent.
These are some of the "special cases" of the Brianchon's Theorem:

Given five straight lines,
show that additional straight lines may be added to envelope a conic.

Construct the conic given five tangents.

Construct the conic given four tangents and one point of contact.

Construct the conic given three tangents and two points of contact.