Central Angle
From Latin: centrum "center"
Definition: The angle subtended
at the center of a circle by two given points on the circle.
Try this Drag any orange dot. Note that when moving the points A or B the angle at the center changes.
Given two points A and B, lines from them to center of the circle form the central angle ∠AOB.
The central angle is the smaller of the two at the center. It does not mean the
reflex angle
∠AOB.
As you drag the points above, the angle will change to reflect this as it increases through 180°
Arcs and Chords
The two points A and B can be isolated points, or they could be the end points of an
arc
or
chord.
When they are the end points of an arc, the angle is sometimes called the "arc central angle".
Inscribed Angle
A similar concept is the inscribed angle. This is the angle subtended at a point on the circle by the two given points.
See Inscribed Angle definition
The central angle is always twice the inscribed angle.
See Central Angle Theorem.
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Other circle topics
General
Equations of a circle
Angles in a circle
Arcs
(C) 2011 Copyright Math Open Reference. All rights reserved
