Geometry

Question Analysis

The main focus is using the equal - length markings () and the perpendicular at  to apply the properties of a perpendicular bisector and find the length of .

 

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 (here ) is equidistant from the endpoints of a line segment ( and ), and there is a perpendicular from that point to the segment (), then the perpendicular line is the perpendicular bisector of the segment. And any point on the perpendicular bisector is equidistant from the endpoints of the bisected segment.

 

Step - by - Step Solution

1. Since  and

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