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Geometric Construction 12

Let c1 and c2 be two fixed circles. If a point A moves along c1 with
AB and AC tangent to c2, show that BC is tangent to a fixed circle.

Construct an animation demonstrating Poncelet's Porism for circles: If
two circles are so related that a triangle can be inscribed to one and
circumscribed to the other, then there are infinitely many such triangles
can be so drawn.

Modify the above situation to the case when the word "circumscribe" also
means the extension of the sides of the triangle circumscribes the circle.

Construct an animation showing: if two circles are so related that a quadrilateral
can be inscribed to one and circumscribed to the other, then there are
infinitely many such quadrilaterals can be so drawn.

Construct an ellipse according to this figure. How is the tangent to the
ellipse constructed?

Construct an animation illustrating Poncelet Porism for the case of two
ellipses.

Construct an animation illustrating Poncelet Porism for the case of a circle
and its circumscribed parabola.

Construct an animation showing if there exists one inscribed triangle of
a given circle tangent to a fixed given parabola, then there are infinitely
many inscribed triangles of the circle have the same property.

Given a triangle, construct an animation showing all possible parabolas
tangent to the sides of the triangle.