[Wafje]

Interesting, I have always visualized tangent differently. A line perpendicular to the X axis that stops at the intersection with the extension of the radius line.

[daef]

I also always used the perpendicular to x-axis version, but I like this version better bcs the tangent tangents in the point of interrest, plus cotangent and tangent are colinear

[ramesaliyev]

I think its same thing just in another point of view, here i rotate the canvas to explain my thought: https://image.ibb.co/ce0rye/qwe.png