5.2 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 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

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of at least two angles of the triangle. The point where they intersect is the incenter.

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

If m∠CAP = 34°, what is m∠CAB if the triangle is isosceles?

Back

m∠CAB = 68°.

Front

If m∠LJK = 28°, what is m∠MLK in an isosceles triangle?

Back

m∠MLK = 124°.

Front

What are the properties of the circumcenter in relation to triangle types?

Back

In an acute triangle, the circumcenter is inside the triangle; in a right triangle, it is on the hypotenuse; and in an obtuse triangle, it is outside the triangle.

Front

What are the properties of the incenter in relation to triangle types?

Back

The incenter is always located inside the triangle, regardless of the triangle's type.