E and F are points on the sides AB and AC respectively of a $ riangle ABC$ such that $\frac{AE}{EB} = \frac{AF}{FC} = \frac{1}{2}$. Which of the following relation is true?

Question

E and F are points on the sides AB and AC respectively of a $	riangle ABC$ such that $\frac{AE}{EB} = \frac{AF}{FC} = \frac{1}{2}$. Which of the following relation is true?

Accepted Answer

Step 1: $\frac{AE}{EB} = \frac{1}{2} \Rightarrow \frac{AE}{AB} = \frac{1}{3}$. By BPT, $EF \parallel BC$ and $\frac{EF}{BC} = \frac{1}{3} \Rightarrow BC = 3EF$.

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