Geometry

Question Analysis

This question focuses on using the properties of a perpendicular bisector. The main task is to determine the length of  by applying the relevant geometric principle based on the given equal - length segments and the perpendicular relationship.

 

Key Concept Explanation

The perpendicular bisector theorem states that any point on the perpendicular bisector of a line segment is equidistant from the endpoints of that line segment. Here, line  is the perpendicular bisector of  (since  and ), so points on  have equal distances to  and .

 

Step-by-Step Solution

1. Observe the given information: We know that , which indicates that  is the mid - point of , and

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