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 cm, then the length of AB is                                                          [SSC (CGL) 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 \[\Delta AEC.\Delta ABD\approx \Delta AEC\]

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

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

\[\therefore \]      \[AB=10\,\,cm\]