Dilated Steiner Inellipse

It is a factor of $\frac{2}{\sqrt{3}}$ . It is the same as a factor between trisecting circle and incircle radii for an equilateral triangle. It is independent of a triangle, in other words, Steiner inellipse dilated by a factor of $\frac{2}{\sqrt{3}}$ from centroid will trisect sides of any triangle.

Equation for big ellipse $4x^2 + 2xy + 7y^2 -36x -36y + 72 = 0$ and

$a^2=\frac{72}{11-\sqrt{13}}$

$b^2=\frac{72}{11+\sqrt{13}}$

$c_b^2+b^2=a^2$

$c_b=\frac {2 \sqrt{\sqrt{13}}} {\sqrt{3}}$

From https://brilliant.org/problems/complex-ellipse/?ref_id=1595309 find for little ellipse $c_l= \sqrt{\sqrt{13}}$

$\frac{c_b}{c_l}=\frac{2}{\sqrt{3}}$

Answer $2+3=5$ .