Question

1. which point is the center of a circle that contains r, s, and t?

a l
b m
c n
d p

1. when constructing the incenter of a triangle, why do you first construct the angle bisectors of two angles? select the true statement.

a because you need the angle bisectors of all the angles.
b angle bisectors are perpendicular to each other.
c angle bisectors are equidistant from the vertices of the tri
d the intersections of angle bisectors are equidistant from of the triangle.

Explanation:

For question 4, the center of a circle that contains three non - collinear points (in this case \(R\), \(S\), and \(T\)) is the circumcenter. The circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle formed by the three points. In the given figure, point \(N\) is the circumcenter (assuming the perpendicular bisector construction is relevant).

For question 5, the incenter of a triangle is the point of intersection of the angle bisectors of the triangle. The incenter is equidistant from the sides of the triangle. When constructing the incenter, we can construct the angle bisectors of two angles because the intersection of two angle bisectors will give the incenter (the third angle bisector will also pass through this point).

Answer:

1. C. \(N\)
2. D. The intersections of angle bisectors are equidistant from the sides of the triangle.