Geometry

Question Analysis

The main focus of this question is to utilize the property of a perpendicular bisector. Given the perpendicular bisector of , we need 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, since is the perpendicular bisector of (shown by the right - angle at and equal - length markings on and ), we have .

 

Step-by-Step Solution

1. Set up the equation:

Because according to the perpendicular bisector theorem, we can write the equation .

2. Solve for :

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

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