A) \[\frac{{{a}^{2}}}{4}\]
B) \[\frac{{{b}^{2}}}{4}\]
C) \[\frac{{{c}^{2}}}{4}\]
D) \[\frac{{{(a+b)}^{2}}}{4}\]
Correct Answer: C
Solution :
[c]\[AB=c\] |
\[BC=a\] |
\[AC=b\] |
\[AD+DB=AB=c\] |
\[CD\times DE=AD\times BD\] |
\[\frac{AD+DB}{2}\ge \sqrt{AD\times BD}\] \[[\because \,\,\,\,\,AB\ge 4M]\] |
\[\frac{c}{2}\ge \sqrt{CD\times DE}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,CD\times DE\le \frac{{{c}^{2}}}{4}\] |
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