Circumcenter

Front

What is the circumcenter of a triangle?

Back

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

Front

What does the Perpendicular Bisector Theorem state?

Back

The Perpendicular Bisector Theorem states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.

Front

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

Back

The circumcenter is equidistant from all three vertices of the triangle.

Front

If D is the circumcenter, what can be said about segments DA, DB, and DC?

Back

Segments DA, DB, and DC are all equal in length, as they are all radii of the circumcircle.

Front

What is a circumcircle?

Back

A circumcircle is a circle that passes through all the vertices of a polygon, specifically a triangle in this context.

Front

What is the significance of the circumcenter in triangle construction?

Back

The circumcenter is used to construct the circumcircle, which is essential in various geometric constructions and proofs.

Front

In triangle ABC, if D is the circumcenter, what is true about point D?

Back

Point D is equidistant from points A, B, and C.

Front

What is the difference between the circumcenter and the incenter?

Back

The circumcenter is the point where the perpendicular bisectors meet and is equidistant from the vertices, while the incenter is the point where the angle bisectors meet and is equidistant from the sides.

Front

How can you determine if a point is the circumcenter?

Back

A point is the circumcenter if it is equidistant from all three vertices of the triangle.