Geometry

Question Analysis

The main focus is using the perpendicular bisector  of . By the perpendicular bisector theorem, we can set up an equation to find the value of  based on the relationship between the lengths  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, since  is the perpendicular bisector of  (shown by the right - angle at  and equal - length markings on the two parts of the line segment related to ), we have .

 

Step-by-Step Solution

1. Set up the equation:

Because  according to the perpendicular bisector theorem, we get