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

 

Answers (1)

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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