IMAS 2024–2025 — Junior Division — Round 2 Question 5

Question 5

As shown in the diagram below, squares $ABCD$ and $APNM$ are placed side by side, without overlapping. The side length of square $ABCD$ is less than the side length of square $APNM$ and $O$ is the intersection of $BN$ and $AD$.

Question illustration

Only one statement from options (A)–(E) is ALWAYS true. Which one is it?

The areas of triangles $BCD$ and $DON$ are equal.
The area of triangle $BDN$ is less than the area of triangle $BCD$.
The area of triangle $BCD$ is larger than the area of triangle $DPN$.
The area of triangle $BOA$ is less than the area of triangle $DON$.
The areas of triangles $BOA$ and $DON$ are equal.