Understanding Perpendicular Bisectors and Circumcenters

The video tutorial explains the concept of perpendicular bisectors, starting with a segment and then extending to triangles. It describes how a perpendicular bisector divides a segment into two equal parts and is perpendicular to it. The tutorial then explores the perpendicular bisectors of a triangle's sides, showing that they meet at a single point called the circumcenter. The video concludes by questioning whether the circumcenter always lies inside the triangle, which will be addressed in the next part.

What is a key characteristic of a perpendicular bisector of a segment?

• It is longer than the segment.

• It is parallel to the segment.

• It divides the segment into three equal parts.

• It bisects the segment at a right angle.

How many perpendicular bisectors can be drawn in a triangle?

• Three

• Two

• Four

• One

What is the point called where the perpendicular bisectors of a triangle meet?

• Orthocenter

• Circumcenter

• Incenter

• Centroid

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

• It is equidistant from all vertices of the triangle.

• It is the point where angle bisectors meet.

• It divides the triangle into two equal areas.

• It always lies inside the triangle.