Understanding Perpendicular Bisectors and Circumcenters

What is the primary characteristic of a perpendicular bisector in a triangle?

• It always passes through the opposite vertex.

• It is the longest side of the triangle.

• It divides a side into two equal parts and is perpendicular to it.

• It is parallel to one side of the triangle.

What is the circumcenter of a triangle?

• The point where all perpendicular bisectors meet.

• The point where all altitudes meet.

• The point where all angle bisectors meet.

• The point where all medians meet.

What unique property does the circumcenter have in relation to the vertices of a triangle?

• It is equidistant from all sides of the triangle.

• It is equidistant from all vertices of the triangle.

• It is always located inside the triangle.

• It is the midpoint of the longest side.

In an obtuse triangle, where is the circumcenter located?

• Inside the triangle.

• At the midpoint of the hypotenuse.

• On one of the sides of the triangle.

• Outside the triangle.

Does the circumcenter remain equidistant from the vertices in an obtuse triangle?

• No, it is closer to the acute angles.

• No, it is closer to the obtuse angle.

• Yes, it remains equidistant.

• Yes, but only if the triangle is isosceles.