Incenter and Circumcenter

Front

What is the definition of the incenter of a triangle?

Back

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

Front

What is the definition of the circumcenter of a triangle?

Back

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. It 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 relationship between the circumcenter and the vertices of a triangle?

Back

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

Front

What segments intersect at the incenter of a triangle?

Back

The incenter is the intersection of the angle bisectors of the triangle.

Front

What segments intersect at the circumcenter of a triangle?

Back

The circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle.

Front

If a triangle has sides of lengths 6, 8, and 10, what is the circumradius?

Back

The circumradius R can be calculated using the formula R = (abc)/(4A), where A is the area of the triangle. For this triangle, R = 5.

Front

How do you find the area of a triangle using its inradius?

Back

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

Front

What is the semi-perimeter of a triangle?

Back

The semi-perimeter s of a triangle is half the sum of the lengths of its sides, calculated as s = (a + b + c) / 2.

Front

What is the formula for the circumradius of a triangle?

Back

The circumradius R can be calculated using the formula R = (abc)/(4A), where A is the area of the triangle.