points of concurrency-triangles

Front

What is the point of concurrency where the angle bisectors of a triangle intersect?

Back

Incenter

Front

What is the point of concurrency where the perpendicular bisectors of a triangle intersect?

Back

Circumcenter

Front

What is the point of concurrency where the medians of a triangle intersect?

Back

Centroid

Front

What is the point of concurrency where the altitudes of a triangle intersect?

Back

Orthocenter

Front

What is the relationship between the circumcenter and the circumcircle of a triangle?

Back

The circumcenter is the center of the circumcircle, which passes through all three vertices of the triangle.

Front

What is the relationship between the incenter and the incircle of a triangle?

Back

The incenter is the center of the incircle, which is tangent to all three sides of the triangle.

Front

How do you find the circumcenter of a triangle using its vertices?

Back

By finding the intersection of the perpendicular bisectors of at least two sides of the triangle.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the point where the three medians intersect and it divides each median into a 2:1 ratio.

Front

What is the formula for finding the coordinates of the centroid of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

Back

Centroid (G) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Front

What is the definition of a median in a triangle?

Back

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