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 $

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