Circumcenter & Incenter

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 is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

How do you find the circumradius of a triangle?

Back

The circumradius (R) can be found using the formula R = (abc) / (4K), where a, b, and c are the lengths of the sides of the triangle and K is the area of the triangle.

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

What is the relationship between the incenter and the incircle?

Back

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

Front

What is an angle bisector?

Back

An angle bisector is a line or segment that divides an angle into two equal parts.

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

How can you determine the location of the circumcenter in an obtuse triangle?

Back

In an obtuse triangle, the circumcenter lies outside the triangle.

Front

How can you determine the location of the circumcenter in an acute triangle?

Back

In an acute triangle, the circumcenter lies inside the triangle.

Front

How can you determine the location of the circumcenter in a right triangle?

Back

In a right triangle, the circumcenter is located at the midpoint of the hypotenuse.