Circular arc
A straight line that connects the two ends of the arc is known as a chord of a circle.
The length (more precisely, arc length) of an arc of a circle with radius r and subtending an angle θ (measured in radians) with the circle center — i.e., the central angle — is This is because Substituting in the circumference and, with α being the same angle measured in degrees, since θ = α/180π, the arc length equals A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement: For example, if the measure of the angle is 60 degrees and the circumference is 24 inches, then This is so because the circumference of a circle and the degrees of a circle, of which there are always 360, are directly proportional.
The upper half of a circle can be parameterized as Then the arc length from
Using the intersecting chords theorem (also known as power of a point or secant tangent theorem) it is possible to calculate the radius r of a circle given the height H and the width W of an arc: Consider the chord with the same endpoints as the arc.
The length of one part is the sagitta of the arc, H, and the other part is the remainder of the diameter, with length 2r − H. Applying the intersecting chords theorem to these two chords produces whence so The arc, chord, and sagitta derive their names respectively from the Latin words for bow, bowstring, and arrow.
