5.2.4.17 Various problems on the plane

In a triangle \( A B C \), the side \( A B \) has length \( \sqrt{3} \), the height \( C D \) dropped to the side \( A B \) has length 3. The base \( D \) of the height \( C D \) lies on the side \( A B \), the length of the segment \( A D \) is equal to the length of the segment \( B C \). Find the length of side \( A C \).