A) \[A{{D}^{2}}+B{{C}^{2}}\]
B) \[A{{O}^{2}}+O{{C}^{2}}\]
C) \[A{{C}^{2}}+B{{D}^{2}}\]
D) \[4\,\,(A{{O}^{2}}+O{{B}^{2}})\]
Correct Answer: D
Solution :
As diagonals of a rhombus bisect each other at right angles. \[\Rightarrow \]AO = OC and BO = OD Applying Pythagoras theorem to \[\Delta AOB,\]\[\Delta AOD,\]\[\Delta DOC,\]\[\Delta BOC\]and on adding \[A{{B}^{2}}+B{{C}^{2}}+C{{D}^{2}}+A{{D}^{2}}\] \[=2\,\,[A{{O}^{2}}+O{{C}^{2}}+B{{O}^{2}}+D{{O}^{2}}]=2\,\,[2A{{O}^{2}}+2B{{O}^{2}}]\]
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