# A rectangle is inscribed in a circle with a diameter lying along the line $3y=x+7$. If the two adjacent vertices of the rectangle are $(-8,5)\:\:and\:\:(6,5)$  , then the area of the rectangle ( in sq. units ) is : Option 1) $84$ Option 2) $98$ Option 3) $72$ Option 4) $56$

centre of circle

Since AB is horizantal C and D can be taken as $(6,\alpha),(-8,\beta)$

$mid \:\:point \:\:of\:\: AC=\left ( \frac{-8+6}{2},\frac{5+\alpha}{2} \right )=\left ( -1,\frac{5+\alpha}{2} \right )$

this should lie on diameter

$\\3y=x+7=3\left ( \frac{5+\alpha}{2} \right )=-1+7=6\\\\\\\:\frac{5+\alpha}{2}=2\\\\\\\:5+\alpha=4\\\\\\\:\alpha=-1$

$\\c=(5,-1)$

$Area=AB\times BC=\left ( 6-(-8) \right )\left ( 5-(-1) \right )\\\\\\\:(14\times 6)=84$

Option 1)

$84$

Option 2)

$98$

Option 3)

$72$

Option 4)

$56$

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