Question

question 5 of 10 which of the following are properties of the circumcenter of a triangle? check all that apply. a. the circumcenter of a right triangle falls on the side opposite the right angle. b. the circumcenter of a triangle is always inside it. c. the circumcenter is at the intersection of the perpendicular bisectors of the triangles sides. d. the circumcenter is equidistant from each vertex of the triangle.

Explanation:

• For a right - triangle, the circum - center is the mid - point of the hypotenuse (the side opposite the right angle), so A is correct.
• The circum - center of an obtuse - angled triangle is outside the triangle, so B is incorrect.
• By definition, the circum - center is the intersection of the perpendicular bisectors of the sides of a triangle, so C is correct.
• Since the circum - center is the center of the circum - circle which passes through all the vertices of the triangle, it is equidistant from each vertex, so D is correct.

Answer:

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