Circumcenter and Incenter Practice

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

How do you find the inradius of a triangle?

Back

The inradius (r) can be found 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 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

If a triangle has sides of lengths 3, 4, and 5, what is the circumradius?

Back

The circumradius R = (abc) / (4K) = (3*4*5) / (4*6) = 2.5.

Front

If a triangle has an area of 24 and a semi-perimeter of 12, what is the inradius?

Back

The inradius r = A / s = 24 / 12 = 2.

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 formula for the area of a triangle using the inradius?

Back

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