Geometry

Question Analysis

The main focus is applying the perpendicular bisector theorem. Since is the perpendicular bisector of (implied by the right - angle at and equal - length markings), we can find by equating the lengths of and .

 

Key Concept Explanation

The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a line segment, it is equidistant from the endpoints of that line segment. Here, .

 

Step-by-Step Solution

1. Set up the equation:

Because , we have .

2. Solve for :

Subtract

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