Question

2 choose the correct answer.
the point of intersection of the angle bisectors of a triangle is the ____
centroid
incenter
equidistant
circumcenter

1. choose the correct answer.

the circumcenter of a triangle is ____ from each vertex of a triangle.
equidistant
incenter
opposite
centroid

Explanation:

Question 2

To solve this, we recall triangle center definitions:

• Centroid: Intersection of medians.
• Incenter: Intersection of angle bisectors (also center of incircle, equidistant from sides).
• Equidistant: A property, not a center.
• Circumcenter: Intersection of perpendicular bisectors (equidistant from vertices).

Thus, the intersection of angle bisectors is the incenter.

Recall the circumcenter: It is the intersection of perpendicular bisectors of a triangle’s sides. By definition, it is equidistant from all three vertices (as it is the center of the circumscribed circle passing through all vertices). Other options:

• Incenter: Equidistant from sides, not vertices.
• Opposite: Not a valid description.
• Centroid: Intersection of medians, related to mass balance, not equidistant from vertices.

Thus, the circumcenter is equidistant from each vertex.

Answer:

B. incenter

Question 3