Transformation geometry proofs (*please answer with detail)

note: sigma is a reflection...

For the curve , r = ( 2abt, a^2 log t, b^2t^2 ), Show that k = - T = 2abt/(a^2 + 2b^2 + t^2)^2 where k = curvature of the curve, T = torsion of the curve

Differential Geometry (II) Curves in Space Curvature of the Curve Torsion of the Curve For the curve r = ( 2abt, a^2 log t, b^2t^2 ) Show that k = - T = 2abt/(a^2 + 2b^2 + t^2)^2 where k = curvature of the curve T = torsion of the curve

For the curve r = ( √6 at^3, a(1+3t^2), √6 at ), Show that k = - T = 1/[a(3t^2 + 1)^2] where k = curvature of the curve, T = torsion of the curve.

Differential Geometry (I) Curves in Space Curvature of the Curve Torsion of the Curve For the curve r = ( √6 at^3, a(1+3t^2), √6 at ) Show that k = - T = 1/[a(3t^2 + 1)^2] where k = curvature of the curve, T = torsion of the curve

Proof Incircle

Let r be the radius on the incircle of tri ABC and a,b,c be the radii of the excircles opposite vertices A, B, and C, respectively. Ilustrate the fact that 1/r = 1/a + 1/b + 1/c. Also, write a proof of this.

Proof involving isosceles triangle

Prove: The two segments joining the vertex of an isosceles triangle with the trisected points of the base are congruent.