Question

point a is the point of concurrency of the angle bisectors of \\( \triangle def \\). what is the length of za? \\( za = 3cm \\) \\( za = 4cm \\) \\( za = 5cm \\) \\( za = 6cm \\)

Explanation:

Step1: Recall Incenter Property

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

Step2: Identify Perpendicular Segments

Segments \( AZ \), \( AX \), and \( AY \) are perpendicular to the sides of \( \triangle DEF \). From the diagram, \( AX = 3 \, \text{cm} \). Since \( A \) is the incenter, \( AZ = AX \).

Answer:

\( \text{ZA} = 3 \, \text{cm} \) (corresponding to the option "ZA = 3cm")