Calculate Circular Angles
Calculator for the angles at a circle: central angle and chord tangent angle. The central angle spans a circular arc with a chord length s. The chord tangent angle or inscribed angle is the angle between circle and chord. Please enter two values, but not two circular angles. The other values will be calculated.
Formulas:
θ = μ/2
μ = arccos[ ( 2 * r² - s² ) / (2r²) ]
s = √ 2 * r² * [ 1 - cos(μ) ]
r = √ s² / { 2 * [ 1 - cos(μ) ] }
Here you can convert radian into degrees.
The radius of a circle is half the diameter of the circle, i.e., the distance from the center of the circle to the circumference. Radius is Latin and means spoke or ray, because of the many possible lines that can radiate from the center of the circle. A chord is a straight line segment between two points on a circle. Two different radius lines in a circle with a given radius and a specific central angle create a chord of a specific length. The chord length increases at a central angle of 0 to 180 degrees, and then decreases again at exactly the same length. The chord length is therefore exactly the same for 160 degrees as for 200 degrees. Values above 360 degrees can be calculated, but they probably make little sense.
A tangent is a straight line through exactly one point on the circle, so it touches the circle without intersecting it. The chord tangent is a tangent through one of the two points on the circle of the chord above. It doesn't matter which one, as the angle is the same for both. This chord tangent angle is half the central angle. Therefore, it is not the same for a central angle of 160 and 200 degrees. The interpretation of the chord tangent angle for a central angle of 200 degrees, as opposed to 160 degrees, is that this angle then lies on the other side of the chord, so this is in the larger circular segment.
