Junior Mathematical Olympiad, September 2019

Point $D$ lies on side $BC$ of triangle $ABC$. Angle $A$ in triangle $ABD$ is equal to angle $C$ in triangle $ABC$, and angle $A$ in triangle $ACD$ is equal to angle $B$ in triangle $ABC$. The given information is not enough to derive the exact shape of triangle $ABC$. However, you can still derive that one of the given statements below is always false. Which statement is it? By $|AB|$ we denote the length of line segment $AB$.

A) $|AD|<|AC|$ B) $|AC|<|AB|$ C) $|AB|<|BC|$ D) $|AD|\times |CD|<|AB|\times |AC|$ E) $|AB|\times |AC|<|AD|\times |BC|$