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It is false. If it has a triangle as its base it would be a pyramid.
A triangle is 2D, and has a square base. A cone is 3D, and has a circular base.
A right circular cone is perfectly balanced on its circular base. Imagine a cone that has a circular base, but leans to one side - this is a non right circular cone.
A right circular cone balanced on its apex.A right circular cone balanced on its apex.A right circular cone balanced on its apex.A right circular cone balanced on its apex.
In a right circular cone a line from the vertex to the center of the circular base is perpendicular to the base. In an oblique circular cone that same line will not be perpendicular.