Directed Angle

The symbol ∡ABC denotes the directed angle from AB to BC, which is the signed angle through which AB must be rotated about B to coincide with BC. Four points ABCD lie on a circle (i.e., are concyclic) iff ∡ABC=∡ADC. It is also true that

 ∡l_1l_2+∡l_2l_1=0 degrees or 360 degrees.

Three points A, B, and C are collinear iff ∡ABC=0 degrees or 180 degrees. For any four points, A, B, C, and D,


See also

Angle, Collinear, Concyclic, Miquel Equation

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Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 11-15, 1929.

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Directed Angle

Cite this as:

Weisstein, Eric W. "Directed Angle." From MathWorld--A Wolfram Web Resource.

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