incenter and circumcenter Review

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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.C.A.3

Front

What is a key property of the incenter?

Back

The distance from the incenter to each side of the triangle is the same.

Tags

CCSS.HSG.C.A.3

Front

How do 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.

Tags

CCSS.HSG.C.A.3

Front

What is the relationship between the incenter and the triangle's incircle?

Back

The incenter is the center of the incircle, which is the circle inscribed within the triangle that touches all three sides.

Tags

CCSS.HSG.C.A.3

Front

What is the relationship between the circumcenter and the triangle's circumcircle?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Tags

CCSS.HSG.C.A.3

Front

If the lengths of the sides of a triangle are known, how can you find the inradius?

Back

The inradius 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 semi-perimeter of a triangle?

Back

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

Tags

CCSS.4.MD.A.3

Front

What is the formula for the area of a triangle using the 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.

Tags

CCSS.HSG.SRT.D.9

Front

What is the significance of the circumradius?

Back

The circumradius is the radius of the circumcircle and is the distance from the circumcenter to any vertex of the triangle.

Tags

CCSS.HSG.C.A.3