The orientation of cell division along the long axis of the interphase cell--the century-old Hertwig's rule--has profound roles in tissue proliferation, morphogenesis, architecture and mechanics. In epithelial tissues, the shape of the interphase cell is influenced by cell adhesion, mechanical stress, neighbour topology, and planar polarity pathways. At mitosis, epithelial cells usually adopt a rounded shape to ensure faithful chromosome segregation and to promote morphogenesis. The mechanisms underlying interphase cell shape sensing in tissues are therefore unknown. Here we show that in Drosophila epithelia, tricellular junctions (TCJs) localize force generators, pulling on astral microtubules and orienting cell division via the Dynein-associated protein Mud independently of the classical Pins/Gαi pathway. Moreover, as cells round up during mitosis, TCJs serve as spatial landmarks, encoding information about interphase cell shape anisotropy to orient division in the rounded mitotic cell. Finally, experimental and simulation data show that shape and mechanical strain sensing by the TCJs emerge from a general geometric property of TCJ distributions in epithelial tissues. Thus, in addition to their function as epithelial barrier structures, TCJs serve as polarity cues promoting geometry and mechanical sensing in epithelial tissues.