Question

1. in the context of a circle, what does the internal part refer to?

a. the center of the circle
b. a point outside the circle
c. a point on the circle
d. a point on the tangent line

1. the incenter of a triangle is found at the intersection of the:

a. altitudes
b. medians
c. angle bisectors
d. perpendicular bisectors

1. which of the following is not a method to construct the circumcenter?

a. finding the midpoint of sides
b. constructing the bisectors of right angles
c. using perpendicular bisectors
d. drawing the medians

1. what is an angle bisector?

a. a line or segment that divides an angle into two congruent angles
b. a line or segment that divides a line segment into two equal parts at a 90 - degree angle
c. a line that is perpendicular to an angle
d. a segment that connects the midpoints of two sides of a triangle

1. what is true about the circumcenter of a triangle?

a. it is always on the hypotenuse
b. it is the same as the incenter
c. it is always inside the triangle
d. it is equidistant from all vertices

1. the angle bisectors of a triangle intersect at which point of concurrency?

a. orthocenter
b. incenter
c. circumcenter
d. centroid

1. which type of triangle is the circumcenter located outside of?

a. right triangle
b. obtuse triangle
c. isosceles triangle
d. acute triangle

Explanation:

1. A tangent line touches a circle at exactly one point, called the tangent point.
2. The circumcenter is the intersection of perpendicular bisectors of a triangle's sides.
3. The circumcenter is constructed using perpendicular bisectors (right-angle bisectors) and midpoints; medians are unrelated.
4. An angle bisector splits an angle into two equal (congruent) angles.
5. The circumcenter is equidistant from all three vertices of the triangle.
6. Angle bisectors of a triangle intersect at the incenter.
7. The circumcenter of an obtuse triangle lies outside the triangle.

Answer:

1. d. A point on the tangent line
2. d. Perpendicular bisectors
3. d. Drawing the medians
4. a. A line or segment that divides an angle into two congruent angles
5. d. It is equidistant from all vertices
6. b. Incenter
7. b. Obtuse triangle