question_answer

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, then the length of AB is                                                               [SSC (CGL) Pre 2014]

A) 9 cm                            

B) 10 cm

C) 7 cm                            

D) 8 cm

Correct Answer: B

Solution :

From figure, \[AE=AD+DE\]

\[=5+3=8\,cm\]

\[\angle ABC=\angle CED\]

Now, in \[\Delta ADB\] and \[\Delta ACE,\]

\[\frac{AB}{AE}=\frac{AD}{AC}\]                     [similar triangles]

\[\Rightarrow \]   \[\frac{AB}{8}=\frac{5}{4}\]

\[\Rightarrow \]   \[AB=\frac{8\times 5}{4}=10\]

\[\therefore \]      \[AB=10\,cm\]