Note: Your teacher will grade your response to questions 13–15 to ensure you receive proper credit for your answer.
What are the properties of the circumcenter of a triangle?
The properties of the circumcenter of a triangle are as follows:
1. The circumcenter is the point where the perpendicular bisectors of the three sides of the triangle intersect.
2. The circumcenter is equidistant from the three vertices of the triangle, meaning that the distances from the circumcenter to each vertex are equal.
3. The circumcenter lies on the perpendicular bisectors of the three sides, which means that the line segments joining the circumcenter to each vertex are perpendicular to the respective sides.
4. The circumcenter is always located inside an acute triangle.
5. In an obtuse triangle, the circumcenter lies outside the triangle.
6. In a right triangle, the circumcenter coincides with the midpoint of the hypotenuse.
7. The circumcenter is the center of the circumcircle, which is the unique circle that passes through all three vertices of the triangle.
8. The distance between the circumcenter and any vertex is equal to the radius of the circumcircle.