def test_solve_biquadratic():
x0, y0, x1, y1, r = symbols('x0 y0 x1 y1 r')
f_1 = (x - 1)**2 + (y - 1)**2 - r**2
f_2 = (x - 2)**2 + (y - 2)**2 - r**2
assert solve_poly_system([f_1, f_2], x, y) == \
[(S(3)/2 - sqrt(-1 + 2*r**2)/2, S(3)/2 + sqrt(-1 + 2*r**2)/2),
(S(3)/2 + sqrt(-1 + 2*r**2)/2, S(3)/2 - sqrt(-1 + 2*r**2)/2)]
f_1 = (x - 1)**2 + (y - 2)**2 - r**2
f_2 = (x - 1)**2 + (y - 1)**2 - r**2
assert solve_poly_system([f_1, f_2], x, y) == \
[(1 - sqrt(((2*r - 1)*(2*r + 1)))/2, S(3)/2),
(1 + sqrt(((2*r - 1)*(2*r + 1)))/2, S(3)/2)]
query = lambda expr: expr.is_Pow and expr.exp is S.Half
f_1 = (x - 1 )**2 + (y - 2)**2 - r**2
f_2 = (x - x1)**2 + (y - 1)**2 - r**2
result = solve_poly_system([f_1, f_2], x, y)
assert len(result) == 2 and all(len(r) == 2 for r in result)
assert all(r.count(query) == 1 for r in flatten(result))
f_1 = (x - x0)**2 + (y - y0)**2 - r**2
f_2 = (x - x1)**2 + (y - y1)**2 - r**2
result = solve_poly_system([f_1, f_2], x, y)
assert len(result) == 2 and all(len(r) == 2 for r in result)
assert all(len(r.find(query)) == 1 for r in flatten(result))
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