Triangle circumcenter and 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 the vertices of the triangle.

Front

How can 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 incenter of a triangle?

Back

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

Front

How can you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of the triangle's angles. The point where they intersect is the incenter.

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

What is the relationship between the incenter and the sides of a triangle?

Back

The incenter is equidistant from all three sides 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.

Front

What is the significance of the inradius?

Back

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

Front

How do you calculate the circumradius of a triangle?

Back

The circumradius (R) can be calculated 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

How do you calculate the inradius of a triangle?

Back

The inradius (r) can be calculated using the formula r = A / s, where A is the area of the triangle and s is the semi-perimeter.