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.

 

Step - by - Step Solution

1. Notice that is the angle bisector of the relevant angle, and and are the perpendicular distances from a point () to the two sides of the angle formed by the angle bisector.

2. According to the Angle Bisector Equidistant Theorem, if a point is on the angle bisector,  the distances from any other point on the non - bisector lines to the two sides of the angle (along perpendiculars) are equal.

3. Here, since , and

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