| 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] |
| \[\Rightarrow \] \[\frac{AB}{8}=\frac{5}{4}\] |
| \[\Rightarrow \] \[AB=\frac{8\times 5}{4}=10\] |
| \[\therefore \] \[AB=10\,cm\] |
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