question_answer

In given figure, O is a point in the interior of a\[\Delta \,ABCD\], \[OD\bot BC,\text{ }OE\bot AC\] and \[OF\bot AB\]. Then:                         

A)  \[O{{A}^{2}}+O{{B}^{2}}+O{{C}^{2}}-O{{D}^{2}}-O{{E}^{2}}-O{{F}^{2}}\]\[=A{{F}^{2}}+B{{D}^{2}}+C{{E}^{2}}\]  

B) \[A{{F}^{2}}+B{{D}^{2}}+C{{E}^{2}}=A{{E}^{2}}+C{{D}^{2}}\]                        

C)  \[O{{A}^{2}}+O{{B}^{2}}+O{{D}^{2}}=O{{E}^{2}}+O{{F}^{2}}+O{{C}^{2}}\]               

D) \[A{{F}^{2}}+A{{E}^{2}}=B{{D}^{2}}+C{{D}^{2}}\]