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