Arc Length

[yellowho]

I'm very confused with the concept of arc length

Suppose radius of the circle is 2. Can you really find find arc length BC. I ran across a problem that suggest you can. It doesn't have to "pivot" from the center?

[Anurag@Gurome]

The arc BC subtends an angle of 40 degrees at the perimeter of the circle. Hence, it will subtend an angle of 80 degrees at the center of the circle.

Hence, arc length BC = (Perimeter of the circle/360)*80

If we have the radius, we can easily find the perimeter of the circle and the arc length BC.

If radius = 2, arc length BC = (2*Ï€*2/360)*80 = 8Ï€/9

[GMATGuruNY]

I'm very confused with the concept of arc length

Suppose radius of the circle is 2. Can you really find find arc length BC. I ran across a problem that suggest you can. It doesn't have to "pivot" from the center?

A central angle is formed by two radii.
An inscribed angle is formed by two chords.
When an inscribed angle and a central angle intercept the same arc on the circle, the degree measurement of the inscribed angle is 1/2 the degree measurement of the central angle:



Circles display the following proportionality:

(Central Angle)/360 = (intercepted arc length)/circumference = (sector area)/(circle area)

Here's a drawing of your problem:



The inscribed angle and the central angle intercept the same arc.
Since the inscribed angle = 40, the central angle = 80.
Thus, the intercepted arc = 80/360 = 2/9 of the circumference.
Since the circumference of the circle = 4Ï€, the arc length = 2/9 * 4Ï€ = (8/9)Ï€.