Segments AB and CD intersect at point O, which is the middle of each of them. What is the segment BD if the segment AC = 7 cm?

To solve the problem, you need to connect points A and C, and points B and D. You get 2 triangles – OAC and OBD. In these triangles OC = OD and AO = OB (since by condition O is the middle of AB and CD). The COA is equal to the BOD because they are vertical. Triangle OAC = OBD triangle by 1 feature (that is, by 2 equal sides and the angle between them). Equal triangles have equal sides opposite equal angles. Therefore AC = BD = 7 cm, since these sides lie opposite the equal angles COA and BOD.
Answer 7 cm.