The radian measure of an angle is the ratio of the length of the arc (s) whose centre is at the vertex of the angle to the radius (r).
If s = r,
One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
$ \displaystyle \text{central angle}=\frac{{\text{length}\ \text{of}\ \text{arc }AB}}{{\text{length}\ \text{of}\ \text{radius}}}=\frac{s}{r}=\frac{r}{r}=1\ \text{radian}$
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