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Only 2 altitudes can intersect at a point.

* * * * *

True but even they do not meet in the interior.

The altitudes of a right angles triangle meet at the right angled vertex. The vertex is at the boundary of the triangle, not in the interior.

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Q: Can the altitudes of a right triangle intersect in the interior of the triangle?
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Can an angle bisector of a triangle always intersect inside the triangle?

The angle bisectors always intersect inside the triangle. (This is not true for altitudes and right bisectors.)


Where is the orthocenter of a right triangle located?

When the triangle is right, the orthocenter is the polygon vertex of the right angle. Intuitively this makes sense because the orthocenter is where the altitudes intersect. Hence, in a right triangle, the vertex of the right angle is where you would expect the altitudes to meet, at 90 degrees, where the legs of the right triangle are perpendicular.


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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.


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Does every triangle have three altitudes?

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true