Perpendicular and Angle Bisectors of a Triangle

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 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.

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 incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of all three angles of the triangle. The point where they intersect is the incenter.

Front

What is an angle bisector?

Back

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

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

What is the relationship between the circumcenter and the circumradius?

Back

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

Front

What is the relationship between the incenter and the inradius?

Back

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

Front

How can the Pythagorean theorem be applied in triangle problems?

Back

The Pythagorean theorem can be used to find the lengths of sides in right triangles, and it can also help in finding distances between points in coordinate geometry.

Front

What is the formula for the circumradius (R) of a triangle?

Back

The circumradius R can be calculated 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.