Geometry

Question Analysis

This question is about applying the Angle Bisector Equidistant Theorem. The main focus is using the congruence of angles  and  to find the length of  based on the known length of .

 

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. Here, since ,  is the angle bisector of . Points on  (such as ) have equal perpendicular distances to  and .

 

Step - by - Step Solution

1. Given that , we can conclude that  is the angle bisector of .

2.  and  are the perpendicular distances from point  (a point on the angle bisector

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