# Geometric Construction 11

Construct the anti-parallelogram (also known as the contra-parallelogram).

Show that the lemniscate of Bernoulli can be drawn with the anti-parallelogram.

Show that the conics can be associated with the aniti-parallelogram.

Construct the tangent to the conics formed as above.

Construct the tangent to the lemniscate of Bernoulli.

Construct two circles of the same radius with each rotating about a point not located at the center while remaining tangent to each other.

Can you change the above construction to allow two circles of different radii?

Instead of two circles tangent to each other exteriorly, make the two circles tangent to each other internally.

Construct two identical ellipses with each rotating about one of its two foci while remaining tangent to each other.

Construct Peaucellier's cell.

Construct the Sylvester-Kempe linkage as follows:
• Construct a "kite".
• Rotate two adjacent sides by 90 degrees as thus.
• Add a side perpendicular to one side of the kite and perpendicular to it.
• Add another link making the shaded region a parallelogram.
• The length of the solid line now remains constant.
• Bend the solid line into two mutually perpendicular lines.
• The linkage is now complete.

Design the linkage according to this figure:

Construct a linkage to draw the cardioid.

Construct a linkage to draw the nephroid.