In Jsxgraph "Intersection" is defined as :
An intersection point is a point which lives on two JSXGraph elements,
i.e. it is one point of the the set
consisting of the intersection points of the two elements. The following
element types can be (mutually) intersected: line, circle,
curve, polygon, polygonal chain.
In the attach file it does not works as expected for all objects. I am surprised. For instance polygon-polygon intersection has no return.