Quantitative Aptitude Ques 24
Question: AD is perpendicular to the internal bisector of $ \angle ABC $ of $ \Delta ABC. $ DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm) is
Options:
A) 4
B) 8
C) 3
D) 6
Show Answer
Answer:
Correct Answer: D
Solution:
- Let AD meet BC at F. $ \angle ADB=\angle BDF=90{}^\circ $ As BD is angle bisector. Let $ \angle DBF=\angle ABD=x $ So, $ \angle BAD=\angle BFD $
$ \therefore $ $ \Delta ABD $ and $ \Delta FBD $ are congruent Now, $ \Delta ADE $ is similar to $ \Delta AFC. $ $ [\because DE\parallel BC] $
$ \therefore $ $ \frac{AE}{AC}=\frac{AD}{AF}=\frac{1}{2} $
$ \Rightarrow $ $ AE=\frac{1}{2}AC=\frac{1}{2}\times 12=6,cm $
BETA
