Hi,

when trying to compute the intersection points of 2 circles i got
strange results.

Example 1:

c1(x,y)=(x-5)^2+y^2-25; c2(x,y)=(y-3)^2+x^2-9
solve([c1(x,y)==0,c2(x,y)==0],x,y)

produces the expected result:

[[x == (45/17), y == (75/17)], [x == 0, y == 0]]


Example 2:
(circle 1 smaller)

c1(x,y)=(x-5)^2+y^2-16; c2(x,y)=(y-3)^2+x^2-9
solve([c1(x,y)==0,c2(x,y)==0],x,y)

produces the unexpected result:

[]

whereas intersection points do exist, e.g.
x=(-9(sqrt(55)-15)/68, y=(-3(sqrt(55)-41)/68

Is it because Example 1 has a rational result, whereas Examples 2 has
an irrational one?

Thanks for any help.

Markus

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