angle ABO = angle DCO
angle AOB = angle DOC
because vertical angles are congruent.
So, triangle ABO is similar to triangle DOC
because two of their three angles are equal each to each.
The two triangles are similar, and hence, proportional.
(here, be careful in your choosing what sides are corresponding to each triangles. For a guide, use the two congruent angles ABO and CDO.)
AB/BO = CD/CO
12/10 = CD/12
10(CD) = 12(12)
CD = 144/10 = 14.4 cm ------answer.