Geometry

Question Analysis

The main focus is using the fact that ∠ROQ = ∠POQ (indicating  is an angle - bisector) and the Angle Bisector Equidistant Theorem to find the value of  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. Since m∠ROQ = m∠POQ,  bisects ∠ROP, so the perpendicular distances from  to  () and from  to  () are equal.

 

Step - by - Step Solution

1. Because  bisects ∠ROP, by the Angle Bisector Equidistant Theorem, .

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