Kasey Nored


Our problem is given points A, B and C, draw a line XY such that AX = XY = YC

Picture 2.png

First we pick an arbitrary point, letŐs say D.

Picture 3.png


Draw a circle with its center at D and radius DA.


Picture 4.png


Construct a parallel line through D being parallel to CB.


Picture 5.png


Construct the intersection of our parallel line and our circle, E and our circle and the segment CB, F.

Picture 6.png


Construct the segment DF and a line parallel to DF through E.   We now have constructed a rhombus DEGF.

Picture 7.png


Constructing Circle F and Circle G provides a better visual that DEGF is actually a rhombus.

Picture 9.png


We can translate our original rhombus to find the points X and Y that meets our original conditions.

Picture 10.png


This is a bit messy, if we hide Rhombus DEGF we can begin to see that our Rhombus that meets the conditions of the problem.   Construction of Circle Y assists in the visual.

Picture 11.png


The segment AX is a radius of circle X, segment XY is a radius of circle X and Y. Segment YB is a radius of circle Y.  AX = XY = YB.