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
the center of the circumcircle of a triangle is known as the
the point of concurrency of the medians in a triangle is known as the
the perpendicular bisector of a side of a triangle is a line segment that is to the side and passes through its midpoint.
the angle bisector of an angle in a triangle divides the angle into two angles.
the incenter of a triangle is equidistant to all
the circumradius of a triangle is equal to half of the of the triangle.

Explanation:

• Angle bisectors intersection: The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all sides of the triangle.
• Inscribed circle: The incircle is the circle that is inscribed within a triangle. Its center is the incenter.
• Perpendicular bisectors intersection: The circumcenter is the point where the perpendicular bisectors of a triangle intersect. It is equidistant from all vertices of the triangle.
• Circle through vertices: The circumcircle is the circle that passes through all three vertices of a triangle. Its center is the circumcenter.
• Medians intersection: The centroid is the point where the medians of a triangle intersect. It divides each median in a 2:1 ratio.
• Altitudes intersection: The orthocenter is the point where the altitudes of a triangle intersect.
• Vertex to midpoint segment: A median is a line segment joining a vertex of a triangle to the midpoint of the opposite side.
• Incircle center: The incenter is the center of the incircle of a triangle.
• Circumcircle center: The circumcenter is the center of the circumcircle of a triangle.
• Medians concurrency: The centroid is the point of concurrency of the medians in a triangle.
• Perpendicular bisector: The perpendicular bisector of a side of a triangle is a line segment that is perpendicular to the side and passes through its midpoint.
• Angle bisector: The angle bisector of an angle in a triangle divides the angle into two equal angles.
• Incircle property: The incenter of a triangle is equidistant to all sides.
• Circumcircle property: The circumcenter of a triangle is equidistant to all vertices.

Answer:

1. incenter
2. incircle
3. circumcenter
4. circumcircle
5. centroid
6. orthocenter
7. median
8. incenter
9. circumcenter
10. centroid
11. perpendicular; passes
12. two equal
13. sides
14. vertices