Question

question 18 of 44
which of the following is a characteristic of an incenter of a triangle?

a. it is the center of the circle that can be inscribed in a given triangle.
b. it is the point where all the perpendicular bisectors of the triangle meet.
c. it is the center of the only circle that can be circumscribed about the triangle.
d. it is equidistant from all three vertices of the triangle.

Explanation:

• Option A: The incenter of a triangle is the point where the angle bisectors meet, and it is the center of the incircle (the circle inscribed in the triangle). This matches the definition of an incenter.
• Option B: The point where perpendicular bisectors meet is the circumcenter, not the incenter.
• Option C: The center of the circumscribed circle (circumcircle) is the circumcenter, not the incenter.
• Option D: A point equidistant from all three vertices is the circumcenter (since the circumradius is the distance from circumcenter to each vertex), not the incenter.

Answer:

A. It is the center of the circle that can be inscribed in a given triangle.