# Prove arc length of a circle is rθ?

**Proof below:-
**

Say for eg.

**r**is the radius of the circle. We know that, perimeter (arc length of the circle is

**2**

**πr**. In this case, the angle described by the circle is 2π).

In above diagram consider

**s**to be the arc length of the circle and angle described by it is

**θ**. If

**2πr**corresponds to

**2π**then we have the below expression

**2πs = 2πrθ**

Solving the above equation we get

**s=rθ**

Hence proved.

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