Geometry

Question Analysis

This question focuses on leveraging the property of the incenter of a triangle to determine which segment length is equal to , testing knowledge of the incenter's defining characteristics.

 

Key Concept Explanation

The incenter of a triangle is the point of intersection of the angle bisectors and is equidistant from the sides of the triangle. This means that the lengths of the perpendiculars from the incenter to each side of the triangle are equal.

 

Step - by - Step Solution

1. Given that  is the incenter of .

2.  is the perpendicular distance from the incenter  to side .

3.  is the perpendicular distance from the incenter  to side , and  is the perpendicular distance from the incenter  to side .

4. By the fundamental property that the incenter is equidistant from the sides of the triangle,