Geometry

Question Analysis

This question focuses on applying the properties of a perpendicular bisector. The key is to recognize the relationship between the given line segment and the perpendicular bisector to find the unknown length.

 

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, the line containing  is the perpendicular bisector of , which means distances from points on  to  and  are equal.

 

Step-by-Step Solution

1. Notice that  is the perpendicular bisector of  as indicated by the right - angle symbol at  and the equal - length marks on  and .

2. Since point  lies on the perpendicular bisector

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