Let $\mathrm{A}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right),\mathrm{B}\left({\mathrm{x}}_2,{\mathrm{y}}_2\right),\mathrm{C}\left({\mathrm{x}}_3,{\mathrm{y}}_3\right)$ be vertices of triangle ABC with BC= a, AB = c, AC = b. If algebraic sum of perpendicular distance from$\mathrm{L}\left(\frac{3{\mathrm{ax}}_1}{\mathrm{a}+\mathrm{b}+\mathrm{c}},\frac{3{\mathrm{ay}}_1}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\right)$, $\mathrm{M}\left(\frac{3{\mathrm{bx}}_2}{\mathrm{a}+\mathrm{b}+\mathrm{c}},\frac{3{\mathrm{by}}_2}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\right)$,$\mathrm{N}\left(\frac{3{\mathrm{cx}}_3}{\mathrm{a}+\mathrm{b}+\mathrm{c}},\frac{3{\mathrm{cy}}_3}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\right)$ to a variable line is zero then all such lines passes through