Geometry

Question Analysis

The main focus is applying the perpendicular bisector theorem. Given that  is the perpendicular bisector of  (marked by right - angle at  and equal - length segments  and ), we aim to find  and  by first getting 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, point  on the perpendicular bisector  of  makes . Also,  as  is on the perpendicular bisector and divides  equally.

Step-by-Step Solution

1. Since  according to the perpendicular bisector theorem, set up the equation .

2. Solve for :

Subtract  from both sides: