Question

the point where the angle bisectors of a triangle intersect is called the ___.
the circle that is inscribed within a triangle is called the ___.
the point where the perpendicular bisectors of a triangle intersect is called the ___.
the circle that passes through all three vertices of a triangle is called the ___.
the point where the medians of a triangle intersect is called the ___.
the point where the altitudes of a triangle intersect is called the ___.
a line segment joining a vertex of a triangle to the midpoint of the opposite side is called a ___.
the center of the incircle of a triangle is known as the ___

Explanation:

These are basic geometric definitions related to triangles. The in - center is the point of intersection of angle bisectors and the center of the incircle. The circum - center is the intersection of perpendicular bisectors and the center of the circum - circle. The centroid is the intersection of medians, the ortho - center is the intersection of altitudes, and a median is a line segment from a vertex to the mid - point of the opposite side.

Answer:

1. in - center
2. incircle
3. circum - center
4. circumcircle
5. centroid
6. ortho - center
7. median
8. in - center