Circular arc

Arc of length  b

Chord of length  l

If you define any two points on a circle and connect them by stretching them with the center of the circle, the two parts of the circular area that are separated from each other by these routes represent sections of a circle (also called a sector of a circle) two radii "cut out" from a circle. The part of the circular line belonging to a circular sector is called the arc of a circle , the angle between the two radii is called the center angle .

calculation

The length of an arc with the center angle in degrees and the radius is ${\displaystyle b}$ ${\displaystyle \alpha }$ ${\displaystyle r}$

${\displaystyle b=\pi \cdot r\cdot {\frac {\alpha }{\displaystyle 180^{\circ }}}}$.

The area of the corresponding segment of the circle is

${\displaystyle A=\pi \cdot r^{2}\cdot {\frac {\alpha }{\displaystyle 360^{\circ }}}}$.

If the center angle is given in radians , the formulas are ${\displaystyle \alpha }$

${\displaystyle b=r\cdot \alpha \qquad A={\frac {r^{2}\cdot \alpha }{2}}}$.

Inserting the angle or gives the known formulas for the circumference and area of the full circle. ${\displaystyle \alpha =360^{\circ }}$ ${\displaystyle \alpha =2\pi }$

The chord length you get over the following relationship from the arc and radius or directly from the central angle: ${\displaystyle l}$

${\displaystyle l=2\cdot r\cdot \sin \left({\frac {b}{2\cdot r}}\right)=2\cdot r\cdot \sin \left({\frac {\alpha }{2}}\right)}$

See also

• Circle segment is the partial area of ​​a circle that is bounded by an arc and a chord.
• Spherical cap is the partial area of ​​a spherical surface that is limited by a small circle (circle of latitude).
• String instrument The Phonoliszt violina is played with a ring-shaped arc (= bow).

Web links

Wiktionary: circular arc  - explanations of meanings, word origins, synonyms, translations

• Online calculation of circular arcs