A) \[A{{B}^{2}}-B{{D}^{2}}=A{{C}^{2}}-C{{D}^{2}}\]
B) \[A{{B}^{2}}+B{{D}^{2}}=A{{C}^{2}}-C{{D}^{2}}\]
C) \[A{{B}^{2}}+B{{D}^{2}}=A{{C}^{2}}+C{{D}^{2}}\]
D) \[A{{B}^{2}}+A{{C}^{2}}=B{{D}^{2}}+D{{C}^{2}}\]
Correct Answer: A
Solution :
In \[\Delta ABD,\] \[A{{B}^{2}}=A{{D}^{2}}+B{{D}^{2}}\] ...(i) In right angled \[\Delta ACD,\] we have \[A{{C}^{2}}=A{{D}^{2}}+C{{D}^{2}}\] ...(ii) On subtracting Eq. (ii) from Eq. (i), we get \[A{{B}^{2}}-A{{C}^{2}}=B{{D}^{2}}-C{{D}^{2}}\] \[A{{B}^{2}}-B{{D}^{2}}=A{{C}^{2}}-C{{D}^{2}}\]You need to login to perform this action.
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