As you know in Euclid's space (normal plane) each line or circumference can be represented a set of points.
Relative to circle a tangent is a line touching the circumference and being perpendicular to its radius at any given point on that circumference.
If circumfetence is set of points [tex]C[/tex] and tangent [tex]T[/tex] then [tex]C\cap T\neq\emptyset[/tex] similarly if we have set [tex]S[/tex] as secant [tex]C\cap S\neq\emptyset[/tex].
The difference however is in the power of these intersection sets namely, [tex]p(C\cap T)=1[/tex] because tangent is touching the circumference at only one point whereas [tex]p(C\cap S)=2[/tex] because the secant is touching circumference at two different points.
Hope this helps.
