Geometry

Question Analysis

The main focus is determining if there's a perpendicular bisector based on the given information and using its properties to find the length of . The equal - length markings () and the perpendicular at  suggest a possible perpendicular - bisector relationship.

 

Key Concept Explanation

A perpendicular bisector of a line segment is a line that is perpendicular to the segment and divides it into two equal parts. If a point is equidistant from the endpoints of a line segment (here  with ) and there is a perpendicular from that point to the segment (), then the perpendicular line is likely the perpendicular bisector of the segment. Points on the perpendicular bisector are equidistant from the endpoints of the bisected segment, and the bisector splits the segment into two equal sub - segments.

 

Step - by - Step Solution

1. Since  and , we can conclude that  is the perpendicular bisector of .

By the property of the perpendicular bisector, it divides  into two equal parts. So,

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