Construct the bisector for a given angle using just a compass and a straightedge.
A drawing of an angle ist given. The task is to do construct its bisector in with the classic straightedge and compass construction, also known as ruler-and-compass construction. The construction follows these steps:
1. Two arcs are made on each ray of the angle with the same compass opening, which means the two points that are marked on the two rays of the angle have the same distance to the angle's vertex.
2. From each of the marked points on the angle's rays swing an arc between the rays, making sure these arcs intersect at some point.
3. Draw a line from the angle's vertex through the newly formed arc intersection. This line is the angle's bisector.
For an easier problem statement, in addition to the angle itself, other construction elements may be provided:
- a single arc on one of the angle's rays
- both arcs on the angle's rays
- two arcs, one on one of the rays and the corresponding arc that has been swung originating from the respective point on the ray
- all of the arc that have to be swung, so all left to do is to draw the bisector itself
The angle's size can be chosen to be up to 90 degress or up to 170 degrees. The size of the drawing can selected from multiple options. There will always be enough space left on the sheet to allow the full construction.
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