Be an ellipse E of center O, of foci F, F1, of major axis AA1 (OA=a, OF=c), M a point of E, m its projection on AA1, T and N the points where the tangent and the normal in M cut AA1 respectively. How to establish the formulas: NF=c/a*MF; Om*OT=a² ; ON=c²/a²*Om ? Thank you.

A triangle ABC with fixed B and C vertex is considered in the plane, A being variable so that b+c remains constant and equal to a given length L.
We call P, T, T' the points of contact of the exinscrit circle in the angle B with the sides BC, AB and AC respectively.
Show that P is fixed and is one of the vertex of the ellipse described by point A. What are the locus of T and T'? How to animate the drawing when A move ? Thank you.

In the plane, an ABC triangle is considered for the vertices B and C are fixed, A being variable so that b +c remains constant and equal to a given length l. (b=distance(A,C), (c=distance(A,B)
How to show that the product tan(B/2=*tan(C/2) remains constant ?

how to draw and calculate the angle of a dihedral of a regular tetrahedron ? Thank you.

How to draw a circle transfomed by orthogonal affinity to oblique line and k ration ? Thank you.