Trisecting a line segment: The example shown results in trisecting the
line segment in red.
The steps involved are:
- Construct a circle with the radius the length of the segment at each
endpoint (A and B) of the line segment. ( 2 circles total)
- Denote the points at the intersection of the two circles (C and F).
- Construct a line between the top point of intersection (C) of the circles
and the center of the circles (A and B).
- Denote the the points of intersection of this line with the circles (D and
E).
- From these new points, construct line segments to the center of the other
circle. (segments DB and EA)
- Construct two line segments from the center of each circle to the bottom
point of intersection between the two triangles. (Segments AF and BF)
- From the point where the line segments in #5 (DB and AE) intersect the
line segments (AF and BF) from #6 (at points G and H) , construct lines to
the top point of intersection between the two circles (GC and HC).
- Each of these two lines, intersects the original line segment 1/3rd the
distance from their respective endpoint. (Points I and J)
If Geometers Sketchpad available:
GSP Trisecting a Line
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