Angle Bisectors and Incenters

Front

What is an angle bisector?

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

Front

What is the incenter of a triangle?

Back

The incenter of a triangle is the point where the angle bisectors of the triangle intersect, and it is also the center of the circle inscribed within the triangle.

Front

How do you find the incenter of a triangle given its vertices?

Back

To find the incenter, calculate the intersection of the angle bisectors of the triangle's angles.

Front

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

Back

The incenter is equidistant from all three sides of the triangle.

Front

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

Back

Area = 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) is half the sum of the lengths of the triangle's sides: s = (a + b + c) / 2.

Front

If the sides of triangle ABC are 6, 8, and 10, what is the semi-perimeter?

Back

s = (6 + 8 + 10) / 2 = 12.

Front

What is the inradius of a triangle?

Back

The inradius is the radius of the inscribed circle, which is the circle that touches all three sides of the triangle.

Front

How do you calculate the inradius of a triangle?

Back

Inradius (r) = Area / semi-perimeter.

Front

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

Back

The incenter is located at the intersection of the angle bisectors, which means it is influenced by the measures of the triangle's angles.