A) \[\frac{{{a}^{2}}+{{b}^{2}}}{2}\]
B) \[{{a}^{2}}+{{b}^{2}}\]
C) \[2({{a}^{2}}+{{b}^{2}})\]
D) \[4({{a}^{2}}+{{b}^{2}})\]
Correct Answer: C
Solution :
In\[\Delta \,\,APD\], \[\tan {{45}^{o}}=\frac{a}{AP}\Rightarrow AP=a\] and in\[\Delta \,\,BPC\], \[\tan {{45}^{o}}=\frac{b}{PB}\] \[\Rightarrow \] \[PB=b\] \[\therefore \] \[DE=a+b\] and \[CE=b-a\] In\[\Delta \,\,DEC\], \[D{{C}^{2}}=D{{E}^{2}}+E{{C}^{2}}\] \[={{(a+b)}^{2}}+{{(b-a)}^{2}}\] \[=2({{a}^{2}}+{{b}^{2}})\]You need to login to perform this action.
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