Question : In $\triangle$ABC, the bisector of $\angle$BAC intersects BC at D and the circumcircle of $\triangle$ABC at E. If AB : AD = 3 : 5, then AE : AC is:
Option 1: 5 : 3
Option 2: 3 : 2
Option 3: 2 : 3
Option 4: 3 : 5
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Correct Answer: 3 : 5
Solution : Given: AB : AD = 3 : 5 AE is bisector of $\angle$BAC. So, $\angle$BAD = $\angle$CAE $\angle$AEC = $\angle$ABC [As AC is a common segment] $\therefore \triangle$ABD $\sim \triangle$AEC So, $\frac{AB}{AE}=\frac{AD}{AC}$ ⇒ $\frac{AB}{AD}=\frac{AE}{AC}$ $\therefore \frac{AE}{AC}=\frac{3}{5}$ Hence, the correct answer is 3 : 5.
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