Question

1. point a is the incenter of δfgh. find as.

a. 3
b. 2
c. 4
d. 5
(image of triangle fgh with incenter a, right angles at t, r, and the foot on gh, segments labeled 3, 5, etc.)

Explanation:

Step1: Recall Incenter Property

The incenter of a triangle is equidistant from all sides of the triangle. So, the distances from point \( A \) (incenter) to each side (via perpendicular segments) are equal.

Step2: Identify Equal Segments

We see that \( AR = AS \) (since both are perpendicular distances from incenter \( A \) to sides of \( \triangle FGH \)). Given \( AR = 3 \), so \( AS = 3 \).

Answer:

a. 3