HYACINTHOS 2344

[APH]:

>Construct a triangle if you are given the elements:
>
> A, b + R = m, c + R = n.
>

I have solved this problem but with conics (the solution in another time)

For now let me ask an other question:

The circles (A,R), (B,R), (C,R) intersect the extensions of the triangle
sides as in the figure:

Ac Ab
\ /
\ /
\ /
\ /
\/ A
/\
/ \
/ \
/ \
/ \
/ \
Bc---------B------------C----------Cb
/ \
/ \
/ \
/ \
Ba Ca


ABa = c + R, ACa = b + R, BCb = a + R, BAb = c + R, CAc = b + R,
CBc = a + R

Which is the radical center of the circumcircles of the
triangles ABaCa, BCbAb, CAcCBc ? Is it something interesting?

[And of course a locus problem is: if instead of R we have k: fixed,
which is the locus of the radical centers of these circumcircles
as k varies?]

APH