GMAT Math

Here's a DS question. Geometry triangle concept.

Is triangle ABC obtuse angled
I) a^2 + b^2 > c^2
II) The center of the circle circumscribing the triangle does not lie inside the triangle

Please give detailed exp as to why each case is valid or invalid & why a specific option was chosen invalidating the other.
Experts Kindly chip in !

option 1:
We do not know if C is longest side. hence insufficient
option 2:
i)acute angled triangle, the center of the circle circumscribing the triangle lies inside the triangle.
ii)right triangle, the center of the circle circumscribing the triangle lies at the mid point of the hypotenuse.
iii)obtuse angled triangle, the center of the circle circumscribing the triangle lies outside the triangle
from option 2 the ABC can be right or obtuse angled

option 1 and option 2: we cannot conclude anything
hence E