Question

a student draws two arcs with the same radius from point a and point b that intersect each other at point m and point n as shown. if $overleftrightarrow{mn}$ and $overleftrightarrow{ab}$ intersect at point o, which statement is true?
$ao = 2\times ob$
$ob = 2\times om$
$ao = ob$
$ao = om$

Explanation:

Step1: Recall the property of perpendicular bisector

When two arcs of the same radius are drawn from two - points \(A\) and \(B\) and they intersect at \(M\) and \(N\), the line segment \(\overline{MN}\) is the perpendicular bisector of the line segment \(\overline{AB}\).

Step2: Analyze the relationship of line - segments

Since \(\overline{MN}\) is the perpendicular bisector of \(\overline{AB}\), it divides \(\overline{AB}\) into two equal parts at the intersection point \(O\). That is, \(AO = OB\).

Answer:

C. \(AO = OB\)