Geometry

Question Analysis

This question focuses on applying the property of the perpendicular bisector. The main task is to use the relationship between the perpendicular bisector and the line segments in the figure to find the length of .

 

Key Concept Explanation

The perpendicular bisector theorem states that a point on the perpendicular bisector of a line segment is equidistant from the endpoints of that line segment. In this figure, the line containing is the perpendicular bisector of (as indicated by the right - angle at and the equal - length marks on and ).

 

Step-by-Step Solution

1. Observe the figure: Notice the right - angle symbol at and the equal - length markings on and , which shows that is the perpendicular bisector of .

2. Apply the perpendicular bisector theorem: Since point

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