Geometry

Question Analysis

This question focuses on using the property of a perpendicular bisector. The main task is to find the length of  by first determining the value of  based on the equal - length relationship derived from the perpendicular bisector theorem.

 

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. Here, line  is the perpendicular bisector of  (as shown by the right - angle at  and equal - length markings on  and ), so .

 

Step-by-Step Solution

1. Since  according to the perpendicular bisector theorem, we can set up the equation .

2. Solve the equation for :

First, move the  terms to one side and the constants to the other side. Subtract  from both sides:

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