Given a linearly connected domain $\Omega$ homeomorphic to a $2D$ disc $D^2$ with a simple regular ($C^1$ and nowhere vanishing derivative) boundary $\partial\Omega$, find such a circle $\omega(\rho, O)$ that minimizes the following sum of fractions (choose one between all ones having a non-empty intersection with $\Omega$), the condition: ($S$ stands for area)
$$\frac{S_{\omega}}{S_{\omega}+S_{\Omega\cap\omega}}+\frac{S_\Omega}{S_\Omega+S_{\Omega\cap\omega}}\rightarrow \min$$ (depiction is below)
