Triangles - Relationships & Points of Concurrency

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of a triangle intersect. It is equidistant from all three vertices of the triangle.

Front

If G is the centroid of triangle ABC, what is the relationship between AG and GD?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment. Therefore, AG = 2 * GD.

Front

What is the length of BG if G is the centroid and BE = 18?

Back

BG = 12, since the centroid divides the median in a 2:1 ratio.

Front

Define the incenter of a triangle.

Back

The incenter is the point where the three angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

What is a median in a triangle?

Back

A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side.

Front

If D is the circumcenter and DG = 19, what does this imply about the triangle?

Back

It implies that the distance from the circumcenter to vertex G is 19 units, indicating the circumradius of the triangle.

Front

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

Back

The centroid is the average of the coordinates of the vertices of the triangle and divides each median in a 2:1 ratio.

Front

How do you find the length of a median in a triangle?

Back

To find the length of a median, use the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the median and c is the length of the opposite side.

Front

What is the orthocenter of a triangle?

Back

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

Front

What is the relationship between the circumcenter and the circumradius?

Back

The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle, centered at the circumcenter.