Question

1. choose the correct answer.

the incenter theorem states that the incenter of a triangle is equidistant from each ___ of a triangle.
circumscribed
circumcenter
side
vertex

1. choose the correct answer.

a(n) ___ circle is a circle that is contained within a polygon so that the circle intersects each side of the polygon at exactly one point.
incenter
vertex
inscribed
side

Explanation:

• For question 4:
• The incenter of a triangle is the point where the angle - bisectors of the triangle meet.
• By the property of the incenter, it is equidistant from each side of the triangle.
• The circumscribed is related to a circum - circle (a circle passing through the vertices of a polygon). The circumcenter is the center of the circum - circle (equidistant from vertices). A vertex is a corner point of the triangle.
• For question 5:
• An inscribed circle (incircle) of a polygon is a circle that is tangent to each side of the polygon (intersects each side at exactly one point).
• The incenter is the center of the inscribed circle. A vertex is a corner of the polygon. A side is a line segment of the polygon.

Answer:

1. C. side
2. C. inscribed