16 AB || DC AC-7,5 A 4,8 B x O D 12 C

AB||DC, следовательно, треугольники ABO и DCO подобны по двум углам. Составим отношение сторон:

$$\frac{AO}{OC} = \frac{BO}{OD} = \frac{AB}{DC}$$ $$AC = AO+OC = 7.5$$ $$\frac{AO}{OC} = \frac{4.8}{12}$$ $$AO = \frac{4.8}{12}OC$$ $$\frac{4.8}{12}OC + OC = 7.5$$ $$OC = \frac{7.5}{\frac{4.8+12}{12}} = \frac{7.5}{\frac{16.8}{12}} = \frac{7.5 \cdot 12}{16.8} = \frac{90}{16.8} = \frac{75}{14}$$ $$AO = 7.5 - \frac{75}{14} = \frac{105 - 75}{14} = \frac{30}{14} = \frac{15}{7}$$ $$\frac{x}{12} = \frac{AO}{OC}$$ $$\frac{x}{12} = \frac{\frac{15}{7}}{\frac{75}{14}} = \frac{15 \cdot 14}{7 \cdot 75} = \frac{210}{525} = \frac{2}{5}$$ $$x = \frac{2 \cdot 12}{5} = \frac{24}{5} = 4.8$$

Ответ: $$x = 4.8$$