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The answer depends on what point of concurrency you are referring to. There are four segments you could be talking about in triangles. They intersect in different places in different triangles.

Medians--segments from a vertex to the midpoint of the opposite side. In acute, right and obtuse triangles, the point of concurrency of the medians (centroid) is inside the triangle.

Altitudes--perpendicular segments from a vertex to a line containing the opposite side. In an acute triangle, the point of concurrency of the altitudes (orthocenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle.

Perpendicular bisectors of sides--segments perpendicular to each side of the triangle that bisect each side. In an acute triangle, the point of concurrency of the perpendicular bisectors (circumcenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle.

Angle bisectors--segments from a vertex to the opposite side that bisect the angles at the vertices. In acute, right and obtuse triangles, the point of concurrency of the angle bisectors (incenter) is inside the triangle.

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Q: Name all types of triangles for which the point of concurrency is inside the triangle?

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Depends on the point of concurrency of what. The point of concurrency of altitudes will be outside in any obtuse triangle.

circumcenter circumcenter is wrong, it is the incenterbecause the point of concurrency is always on the inside of the triangle.

yes

the point of concurrency of the altitudes of a triangle is called the orthocenter.

The point of concurrency is the point intersection.

the point of concurrency of the altitudes of a triangle is called the orthocenter.

The circumcenter, the incenter is the point of concurrency of the angle bisectors of a triangle.

The point of concurrency of the altitudes in a triangle is the orthocenter, while the point of concurrency for the perpendicular bisectors is the centroid/circumcenter. Sorry if this is late! xD

The bisectors of the three angles of a triangle meet at a single point inside the triangle.

Orthocenter of a triangle

the centroid.

centroid

orthocenter

In short, the orthocenter really has no purpose. There are 4 points of Concurrency in Triangles: 1) The Centroid - the point of concurrency where the 3 medians of a triangle meet. This point is also the triangle's center of gravity. 2) The Circumcenter - the point of concurrency where the perpendicular bisectors of all three sides of the triangle meet. This point is the center of the triangle's circumscribed circle. 3) The Incenter - the point of concurrency where the angle bisectors of all three angles of the triangle meet. Like the circumcenter, the incenter is the center of the inscribed circle of a triangle. 4) The Orthocenter - the point of concurrency where the 3 altitudes of a triangle meet. Unlike the other three points of concurrency, the orthocenter is only there to show that altitudes are concurrent. Thus, bringing me back to the initial statement.

It is the meeting point or point of concurrency of three angle bisectors of a triangle.

incenter of a triangle

the centroid of the medians of the triangle

incenter

The Centroid

the orthocenter

circumcenter

circumcenter

It is the circumcentre.

When you have and obtuse triangle and you are trying to find the Orthocenter

Circumcenter.