Theorems about Triangles Practice Test

In triangle $$ABC$$, point $$D$$ lies on side $$\overline{BC}$$, and $$\overline{AD}$$ is the perpendicular bisector of side $$\overline{BC}$$. If $$AB = 13$$ and $$BD = 5$$, what is the length of side $$\overline{AC}$$?

In the diagram, $\triangle ABC$ is shown in the plane. Segments $AB$ and $AC$ have matching single tick marks, indicating they are congruent. No angle arcs, parallel marks, right-angle boxes, midpoint markings, or lengths are given, and the diagram is not drawn to scale. Which statement must be true?