Intersect Command
From GeoGebra Manual
 Intersect[<Line g>, <Line h>]
 Yields the intersection point of lines g and h.
 Intersect[<Line>, <Conic>]
 Yields all intersection points of the line and conic section (max. 2).
 Intersect[<Line>, <Conic>, <Number n>]
 Yields the n^{th} intersection point of the line and the conic section.
 Intersect[<Conic c1>, <Conic c2>]
 Yields all intersection points of conic sections c1 and c2 (max. 4).
 Intersect[<Conic c1>, <Conic c2>, <Number n>]
 Yields the n^{th} intersection point of conic sections c1 and c2.
 Intersect[<Polynomial f1>, <Polynomial f2>]
 Yields all intersection points of polynomials f1 and f2.
 Intersect[<Polynomial f1>, <Polynomial f2>, <Number n>]
 Yields the n^{th} intersection point of polynomials f1 and f2.
 Intersect[<Polynomial>, <Line>]
 Yields all intersection points of the polynomial and the line.
 Intersect[<Polynomial>,< Line>, <Number n>]
 Yields the n^{th} intersection point of the polynomial and the line.
 Intersect[<Function f>, <Function g>, <Point A>]
 Calculates the intersection point of functions f and g by using a (numerical) iterative method with initial point A.
 Intersect[<Function>, <Line>, <Point A>]
 Calculates the intersection point of the function and the line by using a (numerical) iterative method with initial point A.
 Intersect[<Function f>, <Function g>, <leftx>, <rightx>]
 Calculates the intersection points for the two functions in the given interval.
Note: Also see tool Intersect Two Objects.
Following text is about a feature that is supported only in GeoGebra 4.2.

Following text is about a feature that is supported only in GeoGebra 5.0.
Note: From GeoGebra 5, this command will work with 3D objects as well 