Question

point s is the point of concurrency of the angle bisectors of \\( \triangle wxy \\). what is su? \\( \bigcirc su = 5 \\) \\( \bigcirc su = 7 \\) \\( \bigcirc su = 12 \\) \\( \bigcirc su = 13 \\)

Explanation:

Step1: Recall the Incenter Property

The point of concurrency of angle bisectors (incenter) is equidistant from all sides of the triangle. So, \( SU = ST = SV \).

Step2: Identify the Length of \( ST \)

From the diagram, \( ST = 5 \)? Wait, no, wait. Wait, \( SV \) is... Wait, no, the right angles: \( ST \), \( SV \), \( SU \) are all perpendicular to the sides. Wait, \( ST = 5 \)? Wait, no, looking at the diagram, \( ST \) is 5? Wait, no, \( SV \) is... Wait, the length \( ST \) is 5? Wait, no, the incenter is equidistant from all sides, so \( SU = ST = SV \). Looking at the diagram, \( ST = 5 \)? Wait, no, the segment \( ST \) is 5? Wait, no, the length \( ST \) is 5? Wait, the options: \( SU = 5 \), 7, 12, 13. Wait, \( ST \) is 5? Wait, no, \( SV \) is... Wait, the diagram has \( ST = 5 \), \( SV \) is... Wait, the incenter is equidistant from all sides, so \( SU = ST \). So \( SU = 5 \)? Wait, no, wait, \( ST \) is 5? Wait, the diagram shows \( ST = 5 \), so \( SU = 5 \).

Wait, let's recheck. The point S is the incenter (concurrency of angle bisectors), so it is equidistant from all three sides of the triangle. The distances from S to the sides are \( SV \), \( ST \), and \( SU \), all perpendicular to the sides. So \( SV = ST = SU \). From the diagram, \( ST = 5 \), so \( SU = 5 \)? Wait, but the options have \( SU = 5 \) as an option. Wait, maybe I misread. Wait, the diagram: \( ST \) is 5, \( SV \) is... Wait, the length \( ST \) is 5, so \( SU = 5 \).

Step1: Recall Incenter Property

The incenter (S) is equidistant from all sides of \( \triangle WXY \), so \( SU = ST = SV \).

Step2: Identify \( ST \) Length

From the diagram, \( ST = 5 \), so \( SU = 5 \).

Answer:

\( SU = 5 \) (Option: SU = 5)