Question

select the correct answer from each drop - down menu. triangle abc is given. complete the steps to use a compass and straightedge to construct a circle inscribed in △abc. step 1: construct the angle bisector of angles a and b. step 2: label the intersection of the bisectors d. step 3: construct a line from d that (overline{cb}) label the intersection of this line and (overline{cb}). step 4: set the compass width (db). step 5: draw a circle centered at

Explanation:

Step1: Recall in - circle construction

The in - center of a triangle is the point of intersection of the angle bisectors.

Step2: Understand the next step

After finding the in - center \(D\) (intersection of angle bisectors of \(\angle A\) and \(\angle B\)), we need to construct a perpendicular from \(D\) to one of the sides of the triangle. So, in Step 3, we construct a line from \(D\) that is perpendicular to \(\overline{CB}\).

Step3: Set the compass width

The radius of the incircle is the distance from the in - center to the side of the triangle. After constructing the perpendicular from \(D\) to \(\overline{CB}\), the length of the perpendicular segment (distance from \(D\) to the intersection on \(\overline{CB}\)) is the radius. So, in Step 4, we set the compass width equal to the length of the perpendicular segment from \(D\) to \(\overline{CB}\).

Step4: Draw the circle

The center of the incircle is the in - center \(D\). So, in Step 5, we draw a circle centered at \(D\).

Answer:

Step 3: is perpendicular to; Step 4: equal to the length of the perpendicular from \(D\) to \(\overline{CB}\); Step 5: \(D\)