What happens when you take a contour integral and you place a normal vector everywhere along the contour integral then extend the norm vectors until they create an intersection with another normal vector that is contained in the area of the contour integral? Does this area of math have a specific name or any interesting theorems?

Start with the example of a circle by taking the normal vector then extend the normal vectors and they will all intersect at the center of the circle but nowhere else, right? How do you prove this and what happens as you morph the circle into an ellipse or any function that is differentiable and continuous?

I assume that this is covered in an introductory course of differential geometry and manifolds?!