Geometry

Question Analysis

This question focuses on using the property of the incenter of a triangle to find a segment of equal length to , testing knowledge of the incenter's 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. The distance from the incenter to a side is measured along the perpendicular from the incenter to that side.

 

Step - by - Step Solution

1. Since  is the incenter of , the lengths of the perpendiculars from  to the sides of the triangle are equal.

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 property that the incenter is equidistant from the sides of the triangle,

Click "Show Answer" to reveal the answer and analysis