Circumcenter- Part 1

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

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 the triangle?

Back

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

Front

What is the significance of the circumradius?

Back

The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle. It is the distance from the circumcenter to any vertex.

Front

If Z is the circumcenter of triangle TUV, what can be said about the distances TZ, UZ, and VZ?

Back

TZ, UZ, and VZ are all equal because the circumcenter is equidistant from all vertices of the triangle.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

In triangle TUV, if TZ = 21, what is the circumradius?

Back

The circumradius is 21, as it is the distance from the circumcenter Z to vertex T.

Front

What is the formula for the circumradius (R) of a triangle with sides a, b, c and area A?

Back

R = (abc) / (4A), where a, b, and c are the lengths of the sides of the triangle and A is the area.

Front

What type of triangle has its circumcenter inside the triangle?

Back

An acute triangle has its circumcenter located inside the triangle.

Front

What type of triangle has its circumcenter outside the triangle?

Back

An obtuse triangle has its circumcenter located outside the triangle.