1. ## geometry

how can we prove that length of arc in a circle is equal to radius of circle multiplied by angle between extreme radii or sector?

2. Originally Posted by rohith14
how can we prove that length of arc in a circle is equal to radius of circle multiplied by angle between extreme radii or sector?
for a central angle in a circle, its radian angle measure, $\displaystyle \theta$ , is defined as the ratio of the length of the intercepted arc, $\displaystyle s$ , divided by the length of the radius, $\displaystyle r$ ...

$\displaystyle \theta = \frac{s}{r}$

using that definition, you should be able to arrive at the desired result rather easily.

3. Originally Posted by rohith14
how can we prove that length of arc in a circle is equal to radius of circle multiplied by angle between extreme radii or sector?
It is really a matter of definition as opposed to proof.
One radian is defined to be the measure of a central angle in any circle that subtends an arc of the circle equal in length to the radius of the circle.