Circumcenter

Front

What is a circumcenter?

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 segments are concurrent at the circumcenter?

Back

The circumcenter is the point of concurrency for the perpendicular bisectors of the sides of a triangle.

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 circumcircle?

Back

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

Front

If D is the circumcenter of triangle ABC, what can be said about the distances from D to A, B, and C?

Back

The distances from D to A, B, and C are all equal, meaning DA = DB = DC.

Front

What theorem is used to find lengths using the circumcenter?

Back

The Perpendicular Bisector Theorem can be used to find lengths related to the circumcenter.

Front

If the length of DG is 19 and D is the circumcenter, what does this imply about point G?

Back

Point G is located 19 units away from the circumcenter D.

Front

What is the Perpendicular Bisector Theorem?

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 can the Perpendicular Bisector Theorem be applied to find unknown lengths?

Back

By using the theorem, if a point lies on the perpendicular bisector, you can set the distances to the endpoints equal to each other to solve for unknown lengths.

Front

If HG is found to be 14 using the Perpendicular Bisector Theorem, what does this indicate?

Back

It indicates that the point on the perpendicular bisector is 14 units away from both endpoints H and G.