Question

1. choose the correct answer.

the circumcenter theorem states that the circumcenter of a triangle is equidistant from each

○ inscribed
○ vertex
○ circumcenter
○ side

1. choose the correct answer.

a circle that contains a polygon so that it passes through each vertex of the polygon is a(n)
____ circle.

○ incenter
○ circumcenter
○ inscribed
○ circumscribed

Explanation:

• For question 6: The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. By the Circumcenter Theorem, this point is equidistant from the three vertices of the triangle.
• For question 7: A circumscribed circle (circum - circle) of a polygon is a circle that passes through all the vertices of the polygon. An in - center is related to the inscribed circle (incircle) which is tangent to the sides of the polygon. The circumcenter is a point, not a circle.

Answer:

1. vertex
2. circumscribed