Points of Concurrency in Triangles

The video tutorial explains the four main points of concurrency in triangles: circumcenter, incenter, centroid, and orthocenter. Each point is formed by the intersection of specific lines: perpendicular bisectors for the circumcenter, angle bisectors for the incenter, medians for the centroid, and altitudes for the orthocenter. The circumcenter can be inside, on, or outside the triangle and is equidistant from the vertices. The incenter is always inside and equidistant from the sides. The centroid, also inside, is the center of gravity and divides medians in a 1:2 ratio. The orthocenter's position varies, similar to the circumcenter.

What is the circumcenter of a triangle?

• The point where the perpendicular bisectors meet

• The point where the medians meet

• The point where the angle bisectors meet

• The point where the altitudes meet

Where can the circumcenter be located in relation to the triangle?

• Inside, on, or outside the triangle

• Only on the triangle

• Only inside the triangle

• Only outside the triangle

What is the incenter of a triangle?

• The point where the altitudes meet

• The point where the perpendicular bisectors meet

• The point where the medians meet

• The point where the angle bisectors meet

Which property is true about the incenter?

• It is the center of the circumscribed circle

• It divides the medians into a 1:2 ratio

• It is equidistant from the sides

• It is equidistant from the vertices

What is the centroid of a triangle?

• The point where the perpendicular bisectors meet

• The point where the altitudes meet

• The point where the medians meet

• The point where the angle bisectors meet

What unique property does the centroid have?

• It is the center of gravity

• It can be outside the triangle

• It is the center of the circumscribed circle

• It is equidistant from the sides

How does the centroid divide each median?

• Into two equal parts

• Into a 3:4 ratio

• Into a 1:2 ratio

• Into a 2:3 ratio

What is the orthocenter of a triangle?

• The point where the angle bisectors meet

• The point where the medians meet

• The point where the perpendicular bisectors meet

• The point where the altitudes meet

Where can the orthocenter be located in relation to the triangle?

• Only outside the triangle

• Only on the triangle

• Only inside the triangle

• Inside, on, or outside the triangle

Which point of concurrency is not typically used beyond its definition?

• Incenter

• Circumcenter

• Orthocenter

• Centroid