Question

What are the similarities and differences between a tangent and a sectant?

Answer 1

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 $C$ and tangent $T$ then $C\cap T\neq\emptyset$ similarly if we have set $S$ as secant $C\cap S\neq\emptyset$.

The difference however is in the power of these intersection sets namely, $p(C\cap T)=1$ because tangent is touching the circumference at only one point whereas $p(C\cap S)=2$ because the secant is touching circumference at two different points.

Hope this helps.