Tangent to a quartic (Fran├žois Rideau)

 

François Rideau proposed another problem : the construction of the tangent to the quartic at point T .


This problem is difficult from the mathematical point of view and the confirmation with Cabri is amazing.
Here is the François Rideau's figure:

QuarticFR

Fig Cabri Figure (QuarticFR.fig)

Other loci can be constructed thanks to F. Rideau's figure. The pedal of the nephroïd is a rosace:

Rose

Figure cabri (Rosace.fig)

The pedal of the quartic is a non-regular quadrifolium (four-leafed rose):

Pedal



Figure cabri Figure (Pedal.fig)