...line segments intersect <math>\cal{C}</math> more than twice (i.e. all the red points lie inside <math>\cal{C}</math>). Call the [i]inverse[/i] of a blue ...points on <math>\cal{B} P</math> must also pass through the <math>y</math> red points on <math>\cal{A} P</math> (since otherwise the condition that <math> ...

This solution is shown in the diagram by red curve. Each solution of the system is shown by the point of crosspoint red curve with segment. ...