Question

There is a geometrical relation that arc of circle is equal to the central angle.

And there is another relation that arc of a circle is equal to (radius *arc)

Aren't these two relation conflicting? ​

Answer 1

The measure of an arc refers to the arc length divided by the radius of the circle. The arc measure equals the corresponding central angle measure, in radians. That's why radians are natural: a central angle of one radian will span an arc exactly one radius long.
Is the correct