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\\eq\emptyset` similarly if we have set
`S` as secant
`C\cap S\\eq\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.