Quantitative Aptitude Ques 2039
Question: The bisector of $ \angle BAC $ of $ \Delta ABC $ cuts BC at D and the circumcircle of the triangle at E. If DE = 3 cm, AC = 4 cm and AD = 5 cm, then the length of AB is
Options:
A) 9 cm
B) 10 cm
C) 7 cm
D) 8 cm
Show Answer
Answer:
Correct Answer: B
Solution:
- From figure, $ AE=AD+DE=5+3=8cm $ $ \angle ABC=\angle CED $ Now, In $ \Delta ADB $ and $ \Delta AEC.\Delta ABD\approx \Delta AEC $ $ \frac{AB}{AE}=\frac{AD}{AC} $ [similar triangles]
$ \Rightarrow $ $ \frac{AB}{8}=\frac{5}{4} $
$ \Rightarrow $ $ AB=\frac{8\times 5}{4} $
$ \therefore $ $ AB=10cm $
BETA
