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 incircle of a triangle is tangent to all three

the circumcircle of a triangle passes through all three

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 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 Property: The perpendicular bisector of a side of a triangle is perpendicular to the side and passes through its midpoint.
• Angle Bisector Property: The angle bisector of an angle in a triangle divides the angle into two equal angles.
• Incircle Tangency: The incircle of a triangle is tangent to all three sides.
• Circumcircle Passing Through: The circumcircle of a triangle passes through all three vertices.

Answer:

• The point where the angle bisectors of a triangle intersect is called the incenter.
• The circle that is inscribed within a triangle is called the incircle.
• The point where the perpendicular bisectors of a triangle intersect is called the circumcenter.
• The circle that passes through all three vertices of a triangle is called the circumcircle.
• The point where the medians of a triangle intersect is called the centroid.
• The point where the altitudes of a triangle intersect is called the orthocenter.
• A line segment joining a vertex of a triangle to the midpoint of the opposite side is called a median.
• The center of the incircle of a triangle is known as the incenter.
• The center of the circumcircle of a triangle is known as the circumcenter.
• The point of concurrency of the medians in a triangle is known as the centroid.
• The perpendicular bisector of a side of a triangle is a line segment that is perpendicular to the side and passes through its midpoint.
• The angle bisector of an angle in a triangle divides the angle into two equal angles.
• The incircle of a triangle is tangent to all three sides.
• The circumcircle of a triangle passes through all three vertices.