Geometry

Question Analysis

The main focus is using the fact that  bisects ∠URS and the Angle Bisector Equidistant Theorem to find the length of . We'll first find the value of  from the equal - length relationship and then determine the length of .

 

Key Concept Explanation

The Angle Bisector Equidistant Theorem states that if a ray bisects an angle, then any point on that ray is equidistant from the two sides of the angle. So, if  bisects ∠URS, the perpendicular distances from  to  (i.e., ) and from  to  (i.e., ) are equal.

 

Step - by - Step Solution

1. Since  bisects ∠URS, by the Angle Bisector Equidistant Theorem, .

We know that  and . So, we can set up the equation .

Subtract