1. In triangle $A B C$, a point $D$ is taken on side $A C$. It turns out that $B C>A B=5$, $B D=4$, and triangles $A B D$ and $B C D$ are isosceles. Find $A C$. If there are multiple answers, list them in any order separated by a semicolon.
Answer: $9 ; 10 \| 10 ; 9$