Geometric Constructions 7

Construct
the formation of the envelope of light rays, emitted from a radiant point
source at the cusp of a cardioid, after reflection by the same curve.

Construct
the toothwheel coupling between the deltoid and the 3cusped epicycloid.

Construct
the toothwheel coupling between the deltoid and the cardioid.

Construct
the toothwheel coupling between the deltoid and the nephroid.

Construct
the toothwheel coupling between the deltoid and the astroid.

Construct
the toothwheel coupling between the cardioid and the nephroid.

Construct
the toothwheel coupling between the trochoids.

Construct
two identical cardioids each rotating about its cusp meeting orthogonally
on the line segment joining the cusps.

Let
AB be a fixed diameter of a circle O. Through a variable point C on O construct
two cardioids with AB and BC as tangents and with the cusps at the distance
of 2AB apart.

Construct
similarly for a pair of nephroids.

Construct
similarly for the nephroid and the cardioid.