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One of the diameters of the circle circumscribing the rectangle \mathrm{A B C D} is \mathrm{4 y=x+7}. if \mathrm{A} and \mathrm{b} are (-3,4),(5,4), the area of the rectangle is 

Option: 1

16 sq. units


Option: 2

24 sq. units


Option: 3

32 sq. units


Option: 4

48 sq. units


Answers (1)

best_answer

Let \mathrm{O}(\mathrm{h}, \mathrm{k}) be the centre of the circle

\Rightarrow(\mathrm{h}+3)^{2}=(\mathrm{h}-5)^{2} \Rightarrow \mathrm{h}^{2}+6 \mathrm{~h}+9=\mathrm{h}^{2}-10 \mathrm{~h}+25

\Rightarrow 16 \mathrm{~h}=16 \Rightarrow \mathrm{h}=1
(1, k) lies on \mathrm{4 y=x+7 \Rightarrow k=2}

\mathrm{\mathrm{OB}=\sqrt{(1-5)^{2}+(2-4)^{2}}}
\mathrm{=\sqrt{16+4}=\sqrt{20}=2 \sqrt{5}}

Let E be the mid-point of A B Then E is (1,4)



\Rightarrow \mathrm{OE}=2 \Rightarrow \mathrm{AB}=8 \: and \: \mathrm{BC}=4
\mathrm{\Rightarrow Area =4 \times 8=32 sq. units}.
Hence (C) is the correct answer.

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mansi

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