Question : In a triangle ABC a straight line parallel to BC intersects AB and AC at D and E, respectively. If AB = 2AD, then DE : BC is:
Option 1: 2 : 3
Option 2: 2 : 1
Option 3: 1 : 2
Option 4: 1 : 3
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Correct Answer: 1 : 2
Solution :
AB = 2AD
As $\triangle$ADE ~ $\triangle$ABC,
⇒ $\frac{\text{AD}}{\text{AB}}$ = $\frac{\text{DE}}{\text{BC}}$
⇒ $\frac{1}{2}$ = $\frac{\text{DE}}{\text{BC}}$
⇒ $\frac{\text{DE}}{\text{BC}}$ = $\frac{1}{2}$
Hence, the correct answer is 1 : 2.
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