Nikita began with the figure shown.

Question

Depict an abstract representation of Nikita's geometric endeavour to construct an angle bisector. She commences with two intersecting lines at a point forming an angle. She then places a compass on the intersection, creates an arc which intersects the two rays. The compass is moved to the intersections formed with rays and new arcs are created inside the angle which further intersects. Lastly, she draws a line connecting the intersection of angles to the original intersection point. However, there is an error in one of these steps. Do not include any text on the image.

Nikita began with the figure shown.

Two straight lines A B, B C intersecting at B in an angle.

She completed the following actions to construct the angle bisector of ∠ABC, but made a mistake in one of the steps. Select the step in which her mistake was made.

Step 1: She placed the compass on point B and drew an arc which intersects ray BA at point D and ray BC at point E.
Step 2: Next, she placed the compass on point D and drew an arc on the interior of ∠ABC.
Step 3: Then, she placed the compass on point C and drew an arc on the interior of ∠ABC, which intersects the previous arc.
Step 4: She labeled the intersection of the two arcs as point F and drew the ray BF, which represents the angle bisector of ∠ABC.

Answer 1

Her mistake was made in Step 3: Then, she placed the compass on point C and drew an arc on the interior of ∠ABC, which intersects the previous arc.

The correct step would be to place the compass on point E, which is the intersection of the arc drawn in Step 1, and draw an arc that intersects the previous arc from Step 2.