Geometrical constructions：練習問題

To construct the perpendicular bisector of a line segment \( AB \), arcs are drawn with centers at \( A \) and \( B \). If the length of \( AB \) is \( 10\text{ cm} \), what is the minimum radius the compass must be set to for the arcs to intersect at two points?

In a triangle \( ABC \), a student needs to find the region where a point \( P \) is closer to the side \( AB \) than to the side \( AC \). Which construction line acts as the boundary for this region?

A point P is constructed such that it is equidistant from two points A and B, and also equidistant from two intersecting lines L1 and L2. Which statement accurately describes the location of point P?

Which geometric construction is used to accurately locate the midpoint of a line segment \( AB \) using only a compass and a straightedge?

Consider the geometric construction of a perpendicular line from a point \(P\) to a line segment \(AB\), where point \(P\) does not lie on the line segment. Which of the following is the correct first step using a compass and a straightedge?

Describe the steps to construct the perpendicular bisector of a given line segment AB using only a compass and a straightedge.