question_answer

A circle has two equal chords AB and AC. Chord AD cuts BC in E. If AC = 12 cm. and AE = 8 cm., then AD is equal to

A)  27                         

B)         24

C)  21                         

D)         18  

Correct Answer: D

Solution :

  In \[\Delta {{\,}^{S}}\,ACD\] and ACE. A is common to both and \[\angle D=\angle C\](because \[\angle D=\angle B\]and \[\angle B=\angle C\]) \[\therefore \] \[\Delta {{\,}^{S}}\,ACD\]  and ACE are equiangular \[\therefore \]  \[\frac{AC}{AE}=\frac{AD}{AC}\] or            \[\frac{12}{8}=\frac{AD}{12}\] or            \[8\,AD=12\times 12\] or            \[AD=\frac{12\times 12}{8=18\,cm}\]