Question

question consider this construction, which shows circle m inscribed in triangle def. complete each statement. select the correct answer from each drop - down menu. point is the incenter of triangle def. a radius of the circle is segment

Explanation:

Step1: Recall in - center definition

The in - center of a triangle is the point of intersection of the angle bisectors of the triangle. In the given construction, the angle bisectors of \(\triangle DEF\) intersect at point \(M\). So, the in - center of \(\triangle DEF\) is point \(M\).

Step2: Recall radius definition

A radius of a circle is a line segment from the center of the circle to a point on the circle. In the given figure, \(MH\) (or \(MG\) or \(ML\)) is a line segment from the center \(M\) of the circle to a point on the circle. So, a radius of the circle is segment \(MH\) (or \(MG\) or \(ML\)).

Answer:

Point \(M\) is the incenter of triangle \(DEF\). A radius of the circle is segment \(MH\) (or \(MG\) or \(ML\))