Geometry

Question Analysis

This question involves applying the Angle Bisector Equidistant Theorem. The main focus is to use the fact that is the angle - bisector to find the length of by relating it to the known length in the figure.

 

Key Concept Explanation

The Angle Bisector Equidistant Theorem states that if a point lies on the angle bisector of an angle, then it is equidistant from the two sides of the angle. That is, the perpendicular distances from any point on the angle bisector to the two sides of the angle are equal.

 

Step - by - Step Solution

1. Notice that , so is the angle bisector of .

2. and are the perpendicular distances from point (a point on the angle bisector ) to the two sides and respectively. and .

3. A...