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A rectangle A B C D is inscribed in a ci...

A rectangle `A B C D` is inscribed in a circle with a diameter lying along the line `3y=x+10.` If `A` and `B` are the points `(-6,7)a n d(4,7)` respectively, find the area of the rectangle and equation of the circle.

Text Solution

Verified by Experts

`r^2=PM^2+AM^2`
`r^2=4^2+5^2`
`r^2=16+25`
`r=sqrt41`
equation of circle
`(x+!)^2+(y-3)^2=4`
Area of squarre`=AB*AD`
`=AB*2PM`
...
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Knowledge Check

  • 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

    A
    84
    B
    56
    C
    72
    D
    98

  • A rectangle is inscribed in a circle with a perimeter lying along the line 3y = x+7. If the two adjacement verticles of the rectangle are (-8, 5) and (6,5), then the area of the rectangle ( in sq units) is

    A
    72
    B
    84
    C
    98
    D
    56

  • A rectangle with one side of length 4 cm. is inscribed in a circle of diameter 5 cm. Find, the area of the rectangle.

    A
    `21 cm^(2)`
    B
    `12 cm^(2)`
    C
    `4 cm^(2)`
    D
    `3 cm^(2)`

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