Circumcenter and Incenter 10 Q's

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 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 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 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.

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, meaning the distance from the circumcenter to each vertex is the same.

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, meaning the distance from the incenter to each side is the same.

Front

How can you determine if a triangle is acute, right, or obtuse using the circumcenter?

Back

If the circumcenter lies inside the triangle, it is acute; if it lies on a vertex, it is right; and if it lies outside, it is obtuse.

Front

What is the formula for the area of a triangle using the circumradius?

Back

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

Front

What is the significance of the circumcenter in triangle construction?

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 significance of the incenter in triangle construction?

Back

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