Question

question 4 of 10
which of the following are properties of the circumcenter of a triangle? check all that apply.

a. the circumcenter of an obtuse triangle is always outside it.

b. the circumcenter is equidistant from each side of the triangle.

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.

Explanation:

• Option A: For obtuse triangles, the circumcenter lies outside the triangle as the circumcircle's center must be positioned to enclose the obtuse angle.
• Option B: The point equidistant from each side is the incenter, not the circumcenter, so this is incorrect.
• Option C: By definition, the circumcenter is formed by the intersection of the perpendicular bisectors of a triangle's sides.
• Option D: The circumcenter is the center of the circumcircle passing through all three vertices, so it is equidistant from each vertex (this distance is the circumradius).

Answer:

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