@Natanox "basically" isn't the problem. The "definition" isn't really a definition. As written, the arc could be any length. There's no language to link the arc length to the radius, which are equal for radians.

"The measure of a central angle subtending an arc equal in length to the radius." https://www.collinsdictionary.com/dictionary/english/radian

I highly recommend "The Tau Manifesto" for understanding radians and the unit circle better:
https://tauday.com/tau-manifesto#sec-circles_and_angles