Step 1. Establishing the hypotheses (construction data)
Obviously, the result does not depend on the triangle's position with
respect to a coordinate system in the plane. Thus we assume that the
triangle has as vertices the points of coordinates (0,0), (l,0), (r,s).
Since the triangle is non degenerated, we impose that l , s are not zero.
Let (u,v) be the coordinates of the circle's center. Then:
d((u,v),(r,s)=d((u,v), (O,O)
d((u,v),(l,O)=d((u,v), (O,O)
and thus, the hypotheses are just:
(r-u)2+(s-v)2-[u2+v2]=0
(l-u)2+(O-v)2-[u2+v2]=0
lsh=
since lsh=1 is equivalent to l and s non zero.
Step 2. Formulating the thesis (a wrong conjecture)
Analogously, we can assume the thesis states that the center of the circle lies on the X axis:
v=0
(continues in Next Page)
Back to
ICME8-RECIO home page
Previous Page
(Statement of the Problem)
Next Page (Step 3)