Chapter: Similarity· Mathematics Part 2 (Geometry)
Answer: OD = 12
In \(\Delta AOB\) and \(\Delta COD\): \(\angle AOB \cong \angle COD\) (vertically opposite angles) and \(\angle OAB \cong \angle OCD\) (alternate angles, AB || DC, transversal AC).
\(\therefore \Delta AOB \sim \Delta COD\) (AA test) \(\therefore \dfrac{AO}{OC} = \dfrac{BO}{OD}\) (corresponding sides).
\(\dfrac{6}{9} = \dfrac{8}{OD}\) \(\therefore OD = \dfrac{8 \times 9}{6} = 12\).