They can only intersect at the circumcentre, which is a point outside the triangle, beyond the side opposite the obtuse angle.
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No. Not if the triangle is right angled (the intersection is AT the right vertex) or obtuse angled (intersection outside).
No.
In an obtuse angled triangle, two of them will.
any triangle can contain at most 1 obtuse angle. it is called an obtuse triangle.
No right triangle can have any obtuse angles inside it.