No.
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The angle bisectors always intersect inside the triangle. (This is not true for altitudes and right bisectors.)
The point where the three altitudes of a triangle intersect is called the orthocenter. This can be located either inside or outside of the triangle.
Always.
Yes.
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. It may lie inside, outside, or on the triangle depending on the type of triangle. In an acute triangle, the orthocenter lies inside the triangle; in a right triangle, it is at the vertex opposite the right angle; and in an obtuse triangle, it is outside the triangle.