A) \[A{{B}^{2}}+B{{C}^{2}}=D{{C}^{2}}+D{{A}^{2}}\]
B) \[A{{B}^{2}}+C{{D}^{2}}=B{{C}^{2}}+D{{A}^{2}}\]
C) \[A{{B}^{2}}+A{{D}^{2}}=C{{B}^{2}}+C{{D}^{2}}\]
D) \[A{{B}^{2}}+B{{C}^{2}}=2(D{{C}^{2}}+D{{A}^{2}})\]
Correct Answer: B
Solution :
From right angled triangles \[B{{C}^{2}}=O{{C}^{2}}+O{{B}^{2}}\] ?..(i) \[C{{D}^{2}}=O{{D}^{2}}+O{{C}^{2}}\] ?..(ii) \[A{{D}^{2}}=A{{O}^{2}}+O{{D}^{2}}\] ??(iii) \[A{{B}^{2}}=A{{O}^{2}}+O{{B}^{2}}\] ?..(iv) From equations (ii) and (iv), \[A{{B}^{2}}+C{{D}^{2}}=A{{O}^{2}}+O{{D}^{2}}+O{{C}^{2}}+O{{B}^{2}}\] \[=A{{D}^{2}}+B{{C}^{2}}\]You need to login to perform this action.
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