yellowho wrote: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€.
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