A) AB
B) \[AC\]
C) BC
D) None of these
Correct Answer: C
Solution :
\[B{{C}^{2}}=AC\times DC\] [Given] \[\Rightarrow \] \[\frac{BC}{DC}=\frac{AC}{BC}\] Thus, in \[\Delta ABC\]and \[\Delta BDC,\]we have \[\frac{BC}{DC}=\frac{AC}{BC}\] and \[\angle C=\angle C\] [Common] \[\therefore \] \[\Delta ABC\tilde{\ }\Delta BDC\] [By SAS similarity] \[\Rightarrow \] \[\frac{AC}{BC}=\frac{AB}{BD}\] \[\Rightarrow \] \[\frac{AC}{BC}=\frac{AB}{BD}\] [\[\because \] AB = AC (Given)] \[\Rightarrow \] \[BD=BC\]
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