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Question Number 64138 by Tawa1 last updated on 14/Jul/19

Answered by som(math1967) last updated on 14/Jul/19

$$△ADC\sim △BAC$$$$\therefore \frac{AC}{DC}=\frac{BC}{AC}=\frac{AB}{AD}$$$$\therefore \frac{AC}{DC}=\frac{AB}{AD}=\frac{14}{7}\therefore AC=2DC$$$$Again\frac{AC}{DC}=\frac{BC}{AC}\Rightarrow {AC}^2=BC\times DC$$$${AC}^2=(12+DC)DC★$$$$\Rightarrow {AC}^2=12DC+{DC}^2$$$$\Rightarrow {AC}^2-{DC}^2=12DC$$$$\Rightarrow (AC+DC)(AC-DC)=12DC$$$$\Rightarrow 3DC(AC-DC)=12DC★★$$$$AC-DC=4cm$$$$★BC=BD+DC=12+DC$$$$★★AC+DC=2DC+DC=3DC$$$$$$

Commented by Tawa1 last updated on 16/Jul/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir},\mathrm{i}\mathrm{appreciate}\mathrm{your}\mathrm{effort}.$$

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