Geometry

Question Analysis

The main focus is applying the perpendicular bisector theorem. Since is the perpendicular bisector of (marked by the right - angle at and equal - length segments on and ), we need to find by first determining the value of from the equal - length relationship 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, for line segment with perpendicular bisector , we have .

 

Step-by-Step Solution

1. Set up the equation:

Because according to the perpendicular bisector theorem, we get .

2. Solve for :

Subtract from both sides: , which simplifies to .

Add 23 to both sides: , so

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