Let D be the midpoint of side BC in triangle ABC. Let E be the midpoint of line AD and let F be the intersection of line BE with side AC. Find $\frac{AF}{FC}$.
2026-04-01 00:27:17.1775003237
Let D be the midpoint of BC in triangle ABC. Let E be the midpoint AD, F be the intersection of line BE with side AC. Find $\frac{AF}{FC}$.
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Use Menelaus' Theorem for triangle $ADC$ and line $F-E-B$: $$\frac{AF}{FC}\cdot\frac{CB}{BD}\cdot\frac{DE}{EA}=1$$ $$\frac{AF}{FC}\cdot\frac{2}{1}\cdot\frac{1}{1}=1$$ $$\frac{AF}{FC}=\frac12$$