Points of Concurrency

Front

What is the point called that is equidistant from the sides of a triangle?

Back

Incenter

Front

Define the circumcenter of a triangle.

Back

The circumcenter is the intersection point of the three perpendicular bisectors of a triangle.

Front

If the length of segment DL is 24, what is the length of segment DG if they are in a ratio?

Back

8

Front

In triangle ABC, if G is the centroid and BE = 18, what is the length of segment BG?

Back

12

Front

What type of segments are drawn from the orthocenter of a triangle?

Back

Altitudes

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of the triangle intersect.

Front

What is the relationship between the centroid and the vertices of a triangle?

Back

The centroid divides each median into a ratio of 2:1.

Front

What is the definition of the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect.

Front

How do you find the circumradius of a triangle?

Back

The circumradius can be found using the formula R = (abc)/(4K), where a, b, and c are the sides of the triangle and K is the area.

Front

What is the significance of the incenter in triangle geometry?

Back

The incenter is the center of the circle inscribed within the triangle, touching all three sides.