Question

question 8 of 10
which of the following are properties of the incenter of a triangle? check all that apply.

a. the incenter of a triangle is always inside it.

b. the incenter of a right triangle lies on the side opposite the right angle.

c. the incenter is where all of the bisectors of the angles of the triangle meet.

d. the incenter is where all of the perpendicular bisectors of the sides intersect.

Explanation:

• Option A: The incenter is the center of the incircle, which is always inside the triangle, regardless of the triangle type.
• Option B: The incenter of any triangle, including right triangles, is always inside the triangle, not on a side.
• Option C: By definition, the incenter is the intersection point of a triangle's three angle bisectors.
• Option D: The intersection of perpendicular bisectors of sides is the circumcenter, not the incenter.

Answer:

A. The incenter of a triangle is always inside it.
C. The incenter is where all of the bisectors of the angles of the triangle meet.