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Question Number 160353 by Tawa11 last updated on 28/Nov/21

Answered by mr W last updated on 28/Nov/21

Commented by mr W last updated on 28/Nov/21

$$AC=3$$$$AD=\sqrt{1^2+3^2-2\times 1\times 3\times \frac{1}{2}}=\sqrt{7}$$$$\frac{ED}{DC}=\frac{DC}{AD}\Rightarrow ED=\frac{1}{\sqrt{7}}$$$$\frac{EC}{DC}=\frac{AC}{AD}\Rightarrow EC=\frac{3}{\sqrt{7}}=AF$$$$EF=a=\sqrt{7}-\frac{1}{\sqrt{7}}-\frac{3}{\sqrt{7}}=\frac{3}{\sqrt{7}}$$$$\frac{areasmalltriangle}{areabigtriangle}={\left(\frac{a}{3}\right)}^2=\frac{1}{7}$$

Commented by Tawa11 last updated on 28/Nov/21

$$\mathrm{Wow},\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}.$$

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