How should one join the congregational prayer if it is in the Rukoo' stage? Can we just say the 'Takbeer' and take the Rukoo' position, or do we also have to say "Subhaanak Allaahumma wa Bihamdika ..." and then take the Rukoo' position?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

The Muslim scholars agreed in consensus that the opening supplication before the start of the recitation in the prayer is not among the pillars of the prayer or its obligations. So whoever joins the prayer while the Imaam is in Rukoo' (bowing position), he does not have to recite the opening supplication for the prayer. He directly starts the prayer by saying 'Allaahu Akbar' while in a standing position, and then starts counting his prayer from this Raka'h's. As regards whoever bows down along with the Imaam without starting his prayer by saying 'Allaahu Akbar', then his prayer is void because it is not established in principle, as the Prophet said: "The key to the prayer is purification (ablution) and the prayer starts by saying 'Allaahu Akbar', and finishes by saying 'As-Salaamu Alaykum'." [Abu Daawood and At-Tirmithi]. Therefore, it becomes clear that whoever joins the congregational prayer while in Rukoo', he directly says 'Allaahu Akbar' and then bows down without saying the supplication of the opening of the prayer.

Allaah knows best.