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A rectangle \mathrm{A B C D}  inscribed in a circle with diameter lying along the line \mathrm{3 y=x+16}  if A and B are points (2,3),(2,7) then the area of rectangle is
 

Option: 1

12


Option: 2

18


Option: 3

24


Option: 4

36


Answers (1)

best_answer

Let points \mathrm{C}(\alpha, 7)  and \mathrm{D}(\alpha, 3)  mid point of diagonals intersect at centre of circle

\left(\frac{\alpha+2}{2}, 5\right) \text { lie on } 3 \mathrm{y}=\mathrm{x}+16 \Rightarrow \alpha=-2

Area of rectangle =\mathrm{AD} \times \mathrm{AB}=6 \times 4=24

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