Question

a student wants to construct the perpendicular bisector of $overline{ab}$ using a straightedge and a compass. the student first draws an arc using point $a$ as the center. which
the radius is equal to half the length of $overline{ab}$.
the radius is less than half the length of $overline{ab}$.
the radius is greater than half the length of $overline{ab}$.
the radius is equal to one - third of the length of $overline{ab}$.

Explanation:

在使用直尺和圆规作线段$AB$的垂直平分线时，以点$A$为圆心画弧，半径需大于线段$AB$长度的一半，这样后续以点$B$为圆心画弧才能与之前的弧相交，从而确定垂直平分线上的点。

Answer:

The radius is greater than half the length of $\overline{AB}$.