Understanding Perpendicular Bisectors and Circumcenters

What is the primary property of a perpendicular bisector in relation to a segment?

• It forms a 45-degree angle with the segment.

• It is equidistant from the segment's endpoints.

• It is parallel to the segment.

• It divides the segment into three equal parts.

If a point is equidistant from the endpoints of a segment, what can we conclude about its position?

• It lies on the perpendicular bisector of the segment.

• It is outside the segment.

• It is at the midpoint of the segment.

• It lies on the segment itself.

What is the circumcenter of a triangle?

• The point equidistant from all vertices of the triangle.

• The point equidistant from all sides of the triangle.

• The point where the angle bisectors meet.

• The point where the medians intersect.

Which of the following is true about the circumcenter of a triangle?

• It is the intersection of the medians.

• It is the midpoint of the longest side.

• It is the center of the circumcircle.

• It is always inside the triangle.

What is a circumcircle?

• A circle that passes through all the midpoints of a triangle's sides.

• A circle that passes through all the vertices of a triangle.

• A circle that is tangent to all sides of a triangle.

• A circle that is inscribed within a triangle.

What is the relationship between the circumcenter and the circumradius?

• The circumcenter is the endpoint of the circumradius.

• The circumradius is twice the distance from the circumcenter to the centroid.

• The circumradius is the distance from the circumcenter to any vertex of the triangle.

• The circumcenter is the midpoint of the circumradius.

How can the circumcenter be used to construct a circumcircle?

• By using the circumcenter as a vertex and the circumradius as a side.

• By using the circumcenter as the center and the circumradius as the radius.

• By using the circumcenter as the midpoint and the circumradius as the diameter.

• By using the circumcenter as the endpoint and the circumradius as the chord.

What is the significance of the circumcircle in relation to a triangle?

• It is the circle that passes through all the triangle's vertices.

• It is the circle that is tangent to all the triangle's sides.

• It is the largest circle that can fit inside the triangle.

• It is the smallest circle that can encompass the triangle.

Which of the following statements is true about the circumcenter?

• It is always located at the centroid of the triangle.

• It is equidistant from all vertices of the triangle.

• It is always located at the incenter of the triangle.

• It is equidistant from all sides of the triangle.

What does it mean for a circle to be circumscribed about a triangle?

• The circle is tangent to all sides of the triangle.

• The circle passes through all the vertices of the triangle.

• The circle is inside the triangle.

• The circle is tangent to one side of the triangle.