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Central Angle of an Arc
Definition: The angle subtended by an
arc at the center of the circle of which it is part.
Try this Drag one of the orange dots.
Note how the angle at the center of the circle changes.
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The central angle is the angle at the center that is created by the arc. Note that if the arc is a
major arc, the central angle is
a reflex angle. Drag one of the points far around the circle to see this.
If you know the arc length and radius, the formula for the central angle is:
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where:
L is the arc length
R is the radius of the arc
π is Pi, approximately 3.142
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Intercepted Arc
Sometimes we think of this the other way around. We can start with an angle at the the center of the circle,
extend its legs out to the edge of the circle creating, or "cutting off" an arc.
We call this an 'intercepted arc' or 'the arc intercepted by the angle'.
This is just two ways to think about the same thing: either the arc has a central angle, or an angle creates the arc.
See also
tangent,
secant,
chord,
intersecting chords theorem,
intersecting secants theorem,
radius,
diameter,
area of a circle,
concentric circles,
arc,
arc central angle,
arc peripheral angle,
arc central angle theorem,
arc length,
major/minor arcs,
sector,
annulus,
area of an annulus,
segment,
area of segment,
(C) Copyright John Page 2006
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