Geometry

Question Analysis

This question focuses on applying the property of the perpendicular bisector. The main task is to find the length of by first determining the value of based on the equal - length relationship 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,  the point is equidistant from the endpoints of that line segment. Here, the line containing is the perpendicular bisector of (indicated by the right - angle at and equal - length markings on and ), so .

 

Step-by-Step Solution

1. Set up the equation based on the perpendicular bisector theorem:

Since , we have .

2. Solve the equation for :

Subtract from both sides: , which simplifies to

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