Special Points in Triangles

The video tutorial explains four key points related to triangles: circumcenter, centroid, incenter, and orthocenter. Each point is defined and its properties are discussed. The circumcenter is the intersection of perpendicular bisectors, the centroid is the intersection of medians, the incenter is the intersection of angle bisectors, and the orthocenter is the intersection of altitudes. Additionally, the video highlights the collinearity of the orthocenter, centroid, and circumcenter, and explains how the centroid divides the line joining the orthocenter and circumcenter in a 2:1 ratio.

Why is it important for students to understand the special points in a triangle?

• They are frequently tested in exams.

• They help in understanding other geometric concepts.

• They are used in real-life applications.

• They are part of the school curriculum.

What is the circumcenter of a triangle?

• The point where the altitudes intersect.

• The center of the circle that circumscribes the triangle.

• The point where the medians intersect.

• The center of the circle inscribed in the triangle.

How is the circumcenter of a triangle determined?

• By the intersection of perpendicular bisectors.

• By the intersection of altitudes.

• By the intersection of medians.

• By the intersection of angle bisectors.

What letter is commonly used to denote the circumcenter?

• O

• C

• I

• G

Which point is the center of the circle that circumscribes the triangle?

• Orthocenter

• Circumcenter

• Incenter

• Centroid

What is the role of perpendicular bisectors in determining the circumcenter?

• They intersect at the incenter.

• They intersect at the orthocenter.

• They intersect at the circumcenter.

• They intersect at the centroid.

What is the centroid of a triangle?

• The point where the medians intersect.

• The center of the circle that circumscribes the triangle.

• The point where the altitudes intersect.

• The center of the circle inscribed in the triangle.

How is a median of a triangle defined?

• A line joining a vertex to the opposite side.

• A line joining a vertex to the midpoint of the opposite side.

• A line perpendicular to a side.

• A line bisecting an angle.

What letter is commonly used to denote the centroid?

• O

• C

• I

• G

Which point is the intersection of the medians?

• Incenter

• Centroid

• Circumcenter

• Orthocenter