Ruler and Compass, extra exercises

Allowed tools:

In addition to the previous tools you can now also use:

IconMidpoint or Centre
IconPerpendicular Bisector
Icon Perpendicular Line
Icon Angle Bisector
Icon Parallel Line
Icon Reflect Object in Line

This file contains the new set of tools.

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Construction 8 Copy circle

Start with: A circle c and a point P.

Construct: A new circle having the same radius as the circle c and having the centre P.

You can use the construction above to copy a segment of a given length.

You can now use these tools as well:

IconCircle with Centre and Radius
IconSegment with Given Length from Point

This file has the new set of tools.

Image

Construction 9 Copy angle

Start with: Two rays a and b with a common endpoint P, and a ray c having another endpoint Q.

Construct: A ray d with the endpoint Q such that the angle between c and d is equal to the angle between a and b.

 
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Construction 10 Dividing a segment into three equal parts (trisecting)

Start with: A segment.

Construct: Trisect the segment.

Hint: Start the construction as below.

 

Comment: The task of trisecting an angle would have been just a tad more difficult.

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License