Geometry

Question Analysis

This question centers around the application of the perpendicular bisector concept. The main focus is to utilize the properties related to a perpendicular bisector to determine the length of  based on the given equal - length segments and the perpendicular relationship.

 

Key Concept Explanation

The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of that line segment. In this figure, the line containing  is the perpendicular bisector of  because  and .

 

Step-by-Step Solution

1. Examine the given information: We are given that , which shows that  is the mid - point of , and the right - angle symbol indicates that . So,

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