Circumcenter

Front

Define: CIRCUMCENTER OF A TRIANGLE

Back

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

Front

What is the Perpendicular Bisector Theorem?

Back

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the 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; their intersection 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 Z is the circumcenter of triangle TUV, what can you say about the distances from Z to T, U, and V?

Back

The distances from Z to T, U, and V are all equal.

Front

What is the significance of the circumcircle?

Back

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

Front

If the circumcenter is outside the triangle, what type of triangle is it?

Back

If the circumcenter is outside the triangle, the triangle is obtuse.

Front

If the circumcenter is on a vertex of the triangle, what type of triangle is it?

Back

If the circumcenter is on a vertex, the triangle is right-angled.

Front

Calculate the circumradius if the circumcenter is 17 units away from each vertex.

Back

The circumradius is 17 units.

Front

Use the Perpendicular Bisector Theorem to find the length of segment HG if points H and G are 14 units apart.

Back

HG = 14 units.