Lesson 8 Part 2 The Circumcircle and Its Center

What is the initial step in constructing a circumcenter for a triangle?

• Draw the circumcircle

• Construct two perpendicular bisectors

• Find the midpoint of each side

• Draw the altitudes

Where does the circumcenter of an acute triangle lie?

• Inside the triangle

• Outside the triangle

• On one of the sides

• At a vertex

Where does the circumcenter of an obtuse triangle lie?

• Inside the triangle

• Outside the triangle

• On one of the sides

• At a vertex

For a right triangle, where is its circumcenter located?

• Inside the triangle

• Outside the triangle

• On the hypotenuse

• At the vertex of the right angle

Where is the circumcenter of a right triangle located?

• Inside the triangle

• Outside the triangle

• On the hypotenuse

• At the right angle vertex

What specific point on the hypotenuse of a right triangle is its circumcenter?

• The vertex of the right angle

• The midpoint

• One of the acute angle vertices

• A point that divides the hypotenuse in a 1:2 ratio

What is the relationship between the hypotenuse of a right triangle and its circumcircle?

• The hypotenuse is a chord of the circumcircle.

• The hypotenuse is a radius of the circumcircle.

• The hypotenuse is the diameter of the circumcircle.

• The hypotenuse is tangent to the circumcircle.

Which statement accurately describes a property of the circumcenter of any triangle?

• It is equidistant from all three sides of the triangle.

• It is the intersection point of the angle bisectors.

• It is equidistant from all three vertices of the triangle.

• It always lies inside the triangle.