Question : In $ riangle$ABC, the bisector of $\angle$BAC intersects BC at D and the circumcircle of $ riangle$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

Question

Question : In $ riangle$ABC, the bisector of $\angle$BAC intersects BC at D and the circumcircle of $ riangle$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

Team Careers360 · Accepted Answer

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]
$ herefore riangle$ABD $\sim riangle$AEC
So, $\frac{AB}{AE}=\frac{AD}{AC}$
⇒ $\frac{AB}{AD}=\frac{AE}{AC}$
$ herefore \frac{AE}{AC}=\frac{3}{5}$
Hence, the correct answer is 3 : 5.

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Question : In △ABC, the bisector of ∠BAC intersects BC at D and the circumcircle of △ABC at E. If AB : AD = 3 : 5, then AE : AC is:Option 1: 5 : 3Option 2: 3 : 2Option 3: 2 : 3Option 4: 3 : 5

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Question : In $△$ ABC, the bisector of $∠$ BAC intersects BC at D and the circumcircle of $△$ 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