Definition 1. The shape $S$ with smooth closed boundary $\partial S$ is called light-connected if there are two points $A_{out}$ and $A_{in}$ inside its interior such that all of light rays that diverge from point $A_{out}$ converge at point $A_{in}$. The boundary $\partial S$ is supposed to be reflective: the angle of incidence is equal to the angle of reflection.
Definition 2. Light connected curve $S$ is called strongly light-connected if $A_{out}$ and $A_{in}$ do not coincide.
Hypothesis 1. Circle is not strongly light-connected.
Hypothesis 2. If a curve is strongly light-connected, then it is an ellipse.
What can you say about these hypotheses?