Laci constructed ∠PQR with line segments QC¯¯¯¯¯¯¯¯, AC¯¯¯¯¯¯¯¯, and BC¯¯¯¯¯¯¯¯, as shown in the image. Which line segment is the angle bisector of ∠PQR?

To determine which line segment is the angle bisector of ∠PQR, we must first recall that the angle bisector divides the angle into two equal parts.

Since you mentioned segments QC, AC, BC, and QP, without the visual reference, I cannot see the configuration of these segments. However, I can help you identify the angle bisector based on definitions:

1. **Line segment QP:** This may or may not bisect ∠PQR depending on the positions of points P and R relative to point Q.

2. **Line segment QC:** Similar to QP, this line will only bisect the angle if its position equidistantly divides the angle formed between segments PQ and QR.

3. **Line segment AC:** Without knowing how A relates to points P, Q, and R, it's hard to say if this is the angle bisector.

4. **Line segment BR:** This also depends on how B and R are positioned in relation to points P, Q, and R.

Thus, without the image or additional context, I can’t directly identify which line segment is the angle bisector. If you have any specific coordinates or relationships among the points, I can help you analyze it further. In any case, the proper identification should focus on which segment creates two equal angles with respect to ∠PQR.

If you can clarify the diagram or relationships, I can point out which option is correct!