Where is the circumcenter of any given triangle?
(1 point)
Responses
the point of concurrency of the altitudes of the triangle
the point of concurrency of the altitudes of the triangle
the point of concurrency of the perpendicular bisectors of the sides of the triangle
the point of concurrency of the perpendicular bisectors of the sides of the triangle
the point of concurrency of the bisectors of the angles of the triangle
the point of concurrency of the bisectors of the angles of the triangle
the point of concurrency of the medians of the triangle
The correct answer is:
the point of concurrency of the perpendicular bisectors of the sides of the triangle
The circumcenter of any given triangle is the point of concurrency of the perpendicular bisectors of the sides of the triangle. This means that if you draw a line perpendicular to each side of the triangle at its midpoint, the lines will intersect at the circumcenter.
The circumcenter of a triangle is the point at which the perpendicular bisectors of the sides of the triangle intersect. To find the circumcenter, follow these steps:
1. Draw a triangle.
2. Identify the midpoints of each side of the triangle.
3. Draw a line perpendicular to each side passing through its midpoint.
4. Repeat this process for all three sides of the triangle.
5. The point where all three perpendicular bisectors intersect is the circumcenter of the triangle.
The statement "the point of concurrency of the perpendicular bisectors of the sides of the triangle" is the correct explanation for the location of the circumcenter.