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Question Number 189438 by normans last updated on 16/Mar/23

Answered by som(math1967) last updated on 16/Mar/23

$$constructFM\parallel BE$$$$△AFM\sim △ABE$$$$\frac{AM}{AE}=\frac{3}{3+5}=\frac{3}{8}$$$$\frac{AM}{ME}=\frac{3}{5}$$$$EO\parallel FM$$$$\frac{CE}{EM}=\frac{CO}{OF}$$$$\frac{CE}{EA}=\frac{2}{3}$$$$\frac{CE}{EA}\times \frac{AE}{AM}=\frac{2}{3}\times \frac{8}{3}$$$$\frac{CE}{AM}=\frac{16}{9}$$$$\frac{CE}{AM}\times \frac{AM}{ME}=\frac{16}{9}\times \frac{3}{5}$$$$\frac{CE}{EM}=\frac{16}{15}=\frac{CO}{OF}$$$$\therefore \frac{ar△BFO}{ar△BCO}=\frac{FO}{CO}=\frac{15}{16}$$

Commented by som(math1967) last updated on 16/Mar/23

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