Question

the point where the angle bisectors of a triangle intersect is called the _. the point where the perpendicular bisectors of a triangle intersect is called the _. the incenter is equidistant from all _ of the triangle. the circumcenter is equidistant from all _ of the triangle. the circle that passes through all the vertices of a triangle is called the _. the circle that is tangent to all sides of a triangle is called the _. the perpendicular bisectors of a triangle are used to find the _. the angle bisectors of a triangle are used to find the _.

Explanation:

1. The intersection of angle - bisectors of a triangle is the in - center.
2. The intersection of perpendicular bisectors of a triangle is the circum - center.
3. The in - center is equidistant from all sides of the triangle.
4. The circum - center is equidistant from all vertices of the triangle.
5. The circle passing through all vertices of a triangle is the circum - circle.
6. The circle tangent to all sides of a triangle is the in - circle.
7. Perpendicular bisectors are used to find the circum - center.
8. Angle bisectors are used to find the in - center.

Answer:

1. in - center
2. circum - center
3. sides
4. vertices
5. circum - circle
6. in - circle
7. circum - center
8. in - center