Barrel arc
The barrel arc is a term from geometry . It denotes an arc of a circle over a line from which this line always appears at the same angle. Since there is such a circular arc on each side of the given route, one speaks of a barrel arc pair .
Definition and application
The barrel arc can also be viewed as the geometric location ( set ) of all points from which a chord of the circle can always be seen at the same angle. This particular angle is also called the circumference angle .
A special case of the barrel arc is the Thales semicircle . In this, each circumferential angle measures 90 °, and the chord is the diameter of the circle.
The barrel arc helps prove a number of geometric theorems. For example, the following statement can be proven well with the barrel arc:
In a triangle, the normal perpendicular to one side and the bisector of the opposite angle of the side intersect on the circumference ( south pole set ).
The terms barrel arc and barrel circle are used synonymously.
See also: circle angle
construction
example 1
- Draw string (AB),
- Create the desired barrel angle ( ) at a tendon end point (for example here at A) .
- In the vertex (at A), make the perpendicular on the angle leg.
- Construct the perpendicular for (AB).
The intersection of the vertical and perpendicular results in the center point of the barrel circle (M) (see picture).
Example 2
- Draw string (AB),
- Subtract the circumferential angle ( ) from 90 ° (for an obtuse angle: subtract 90 ° from the circumferential angle) and apply this angle to A and B.
- The intersection of the two free legs is the center of the circumference.
Example 3
- Draw a (circumferential) angle ( ) with point C
- Pick a point A on one leg and draw a circle with radius | AB | around A, this cuts the other leg in B.
- Erect the vertical verticals on AB and AC, these intersect in the center of the barrel circle.
literature
- Günther Aumann: Circular Geometry: An Elementary Introduction . Springer, 2015, ISBN 9783662453063 , pp. 16-17
- Rolf Baumann: More success in mathematics: 8th grade geometry . Mentor, 2008, ISBN 9783580656294 , pp. 78-80
- Siegfried Krauter, Christine Bescherer: The Elementary Geometry Experience: A workbook for independent and active discovery . Springer, 2012, ISBN 9783827430250 , pp. 74-76