Department of Mathematics Education
EMT 469
Begin by copying c.(segmentAB)
Now from point A construct a circle with a radius of length b. This circle
is the locus of all the points that C can be.
Now connect point C with point B and call this segment a. Take the midpoint
of a and connect it with the midpoint of c.
The circle centered at the median of c and going through CB. Thus one
locus for the midpoint of the side oppisite vertex A is this circle:
Another locus of the midpoint of the side opposite vertex A is a circle
with center at A and radius of ma.
Where these two circles intersect is the point at which this triangle
can have a midpoint opposite A.
Thus, the construciton is complete.
For a GSP script click here.
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