A) \[{{b}^{2}}+{{c}^{2}}=b{{'}^{2}}+c{{'}^{2}}\]
B) \[{{c}^{2}}+{{a}^{2}}=c{{'}^{2}}+a{{'}^{2}}\]
C) \[{{a}^{2}}+{{b}^{2}}=a{{'}^{2}}+b{{'}^{2}}\]
D) none of these
Correct Answer: C
Solution :
[c] Since the diagonals are perpendicular, the given quadrilateral is a rhombus. So the distances between two pairs of parallel sides are equal, hence, \[\left| \frac{c'-c}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|=\left| \frac{c'-c}{\sqrt{a{{'}^{2}}+b{{'}^{2}}}} \right|\] Or \[{{a}^{2}}+{{b}^{2}}=a{{'}^{2}}+b{{'}^{2}}\]
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