Question

question 6 of 10 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 triangles sides. b. the circumcenter of a right triangle falls on the side opposite the right angle. c. the circumcenter is equidistant from each vertex of the triangle. d. the circumcenter of a triangle is always inside it.

Explanation:

• A: By definition, the circum - center is the intersection of the perpendicular bisectors of a triangle's sides.
• B: In a right - triangle, the circum - center is the mid - point of the hypotenuse (the side opposite the right angle).
• C: The circum - radius is the distance from the circum - center to each vertex, so the circum - center is equidistant from each vertex.
• D: The circum - center of an obtuse - angled triangle is outside the triangle.

Answer:

A. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.
B. The circumcenter of a right triangle falls on the side opposite the right angle.
C. The circumcenter is equidistant from each vertex of the triangle.