Question

Find the angle subtended at the center by the circumference of the circle.

Answer 1

If $r$ be the radius of the circle, then circumference of the circle = $2\pi r$

Also we know that :

$1$ radian is the measure of an angle subtended at the center of a circle of radius $r$ by an arc of length $r$.

i.e., the angle subtended at the center by an arc of length $r=1$ radian

Angle subtended at the center by an arc of unit length $=\frac{1}{r}$ radian

The angle subtended at the center by arc of length $2\pi r=\frac{1}{r}\times 2\pi r=2\pi$ radians.

Thus, the angle subtended at the center of circle by the circumference $=2\pi$.