Circumcenter

1. The Circumcenter of a triangle can be found as the intersection of any two of the three perpendicular bisectors.

2. A perpendicular bisector is a line that forms a right angle with one of the triangle’s sides and intersects that side at its midpoint.

3. Circumcenter of a triangle is equidistant from the three vertices of the triangle , and it always forms the center of a circumscribed circle containing these three vertices on its circumference.

 

Experiment with free-form simulation,of circumcenter of a triangle, below:

 

Experiment with the above simulation to answer the following questions?

 

 

Q1 Why is Circumcenter of a triangle equidistant from the three vertices of the triangle?

Q2 Can Circumcenter of a triangle lie/exist outside of the triangle? If yes, when? If no, Why?

Q3: Is Circumcenter of a triangle average of all points on that triangle? Why?