Question

Which of the following are properties of the circumcenter of a triangle? Check

all that apply.
A. The circumcenter is at the intersection of the perpendicular
bisectors of the triangle's sides.
B. The circumcenter of an obtuse triangle is always outside it.
M C. The circumcenter is equidistant from each vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.

Answer 1

The circumcenter of a triangle is at the intersection of the triangle's perpendicular bisectors, is equidistant from each vertex, and for an obtuse triangle, it lies outside the triangle.

Step-by-step explanation:

The properties of the circumcenter of a triangle are indeed unique and serve an important role in triangle geometry. The following options are correct:

A. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.

B. The circumcenter of an obtuse triangle is always outside it.

C. The circumcenter is equidistant from each vertex of the triangle.

Option D is not correct because the circumcenter is not equidistant from each side of the triangle; it is equidistant from the triangle's vertices, which is why it is the center of the circle that can be circumscribed around the triangle, known as the circumcircle.